After this you might have some clean-up function to tidy up the resultant expression reducing fractions etc. When your transformation of the s-exp is done, reconvert the resultant s-exp into string form, again with a recursive function.
SLaks already described the procedure for symbolic differentiation. I'd just like to add a few things:. For what kinds of operations are you wanting to compute a derivative? If you allow trigonometric functions like sine, cosine and tangent, these are probably best stored in a table while others like polynomials may be much easier to do. Are you allowing for functions to have multiple inputs,e. Polynomials in a single variable would be my suggestion and then consider adding in trigonometric, logarithmic, exponential and other advanced functions to compute derivatives which may be harder to do.
What's difficult, perhaps counterintuitively, is simplifying the result afterward. To do the differentiation, store the operations in a tree or even just in Polish notation and make a table of the derivative of each of the elementary operations.
Then repeatedly apply the chain rule and the elementary derivatives, together with setting the derivative of a constant to 0. This is fast and easy to implement. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow. Learn more. Derivative Calculator Ask Question. Asked 11 years, 7 months ago. Active 5 years, 1 month ago.
Viewed 15k times. Thanks I'm sorry! I clearly want to make symbolic differentiation. Improve this question. Derivative Calculator This simple and convenient derivative calculator will help you solve any problem, just enter the value of the function and you will immediately get a solution with a detailed step-by-step description. The easy-to-use calculator interface allows you to quickly calculate any functions. Try this handy derivative calc right now! Calculate Derivatives Other Calculators.
How to use the Derivative Calculator Type in a function to solve To get started, type in a value of the function and click submit button. In a moment you will receive the calculation result. See a step-by-step solution After receiving the result, you can see a detailed step-by-step description of the solution. This will help you understand the solution of the problem. Modified Bessel This program will compute values for modified Bessel functions for non-negative order. The user inputs the order and value and the program returns the value, accurate to at least 8 decimal places.
Moving Average 2 This program is designed to compute moving averages when information is in discrete form, not in continuous form as my previous program does. Enter in the information and the spread for the interval. The program will store the averages in L3 and ask you what information you'd like plotted. Be aware that if you start your lists with a zero instead of a one, you'll have to adjust the program a little. Moving Average This program will plot the moving average for a continuous function.
It is slow though. Riemann Sums Given f x , a starting and ending point, and the number of partitions, this program will analyze the area under the curve using Riemann sums from the left, right, midpoint, and a definate integral to check accuracy.
Newtons Method This program allows the user to calculate the end value AND intermediate steps to show "work" on tests, of course of Newton's Method. It has allowed me to brainlessly work out these problems and show that damn work that my teacher requires :- Updated June Newton's Method v1. Newton It may seem like another Newton iteration program, but I've written this one to have a few special touches to it that make it worthwhile.
First, the program displays the equation Y1 upon loading. After asking for an X value to be the starting point, the calculator tests that value. I added the pathological error aspects to this program because the typical Newton iteration program will continuously attempt iterations before the "divide by zero" error is displayed if it ever is , wasting both time and batteries. Newton's Law of Cooling A simple, efficient, and quick way of calculating the temperature of a body using initial temperature, surrounding temperature, time, and a k constant also known as Newton's Law of Cooling!
Newton's Method This program is a Newton's method root finder. It uses Y1 as f x , and shows all steps used. Newton's Method 83p This program finds the roots zeros of a function nearest a user inputed guess. Easy to use. Newton's Method this program helps you do the tedius steps of Newton's Method and saves you lots of time.
Newton's Method of Approximation Whilst sitting in calculus class, I got bored. Naturally I made a program to simplify what we were learning and share it with the class. So here it is, Jorgan Pubshire's official Newton's Method program. This is the best Newton's Method program because not only does it approximate your zero, it also builds your entire information table through what I call a cascading table display.
Also, this program can do an infinite number of iterations. There are two modes in this program: Iteration mode allows you to input a set number of iterations to be ran and Accuracy mode runs iterations until it reaches an accuracy that is set by the user.
My teacher had already made this program a couple years ago and when I gave him my program he admitted that mine was better. There literally is no way to make this program better save converting it into a fancy flash program, but since I can't do that yet, this will have to do.
It will give final temp, a graph, the cooling rate and the time spent. Newton's Method AP Calculus subject: finding the root zero of an equation. Input f x , f' x , and guess, and the program will show you all the work to do to solve the problem. This eliminates all the tedious work and mistakes when doing homework. Newton's Method Newton's Method including all work is performed using Symbolic. Newton's Method This program uses Newton's Method to find roots of a given function. After inputing an initial guess and error, it finds a sequence of estimates and stops when the difference between estimates is less than the given error.
Normal Line This program will output the slope and y-intercept of a normal line. The user enters in the function and the x-coordinate. Great for Calc 1 students. Notes: Differential and Integral Calculus v0.
The two others was more general, but this one is only on the differential and integral calculus. It is very useful for those who are studying these courses.
It contains just the formulas useful for the two mathematics disciplines. There are derivative formulas, integration formulas, identities and some others. More things coming soon! Newton-Raphson Method Visually go through the Newton-Raphson Method and understand how it the process approximates more accurately with each iteration.
It also obtains solutions for a given initial condition using Runge-Kutta. Olver's Root Finder This program uses Olver's cubically convergent method for finding roots. Diff Eq's Help - 2nd Order Nonhomogeneous ODEs Displays several formulae relevant to finding particular solutions to nonhomogeneous second-order linear differential equations.
Includes formulae for the undetermined coefficients and variation of parameters methods for finding particular solutions. Also includes relevant formulae for finding the particular steady state solutions to driven, damped spring-mass systems.
Very fun to play with if Taylor series just aren't good enough for you. Parametic Curve Length This program will compute the length of a curve given in parametric form. Polar Derivatives This program will save you a ton of time when taking derivatives of polar functions. Be warned, although the function will be essentially right, it cannot simplify using trigonometric identities. You must have Symbolic and Prettyprint installed to use this program. Polynomial Division 2. Polyroot This small program calculates the roots of a polynomial by Newton's Method, including quadratic equations.
Check readme for specifics. Pre-Calc My math teacher advised me to submit this, it is very helpful when doing Pre-Calculus problems. Now that my math teacher hates me for creating a program for her students to compute math at ease, she advised me to submit it for the use of other Pre-Calculus students. Well, here you go. This program is very helpful and even has a 2D unit circle for reference when dealing with Unit Circle Trigonometry. Precalculus beta A very helpful program. More features will be added in the final version.
PreCalculus This is a compilation of all my programs from my year studying precalculus. It helped me a lot, and I hope that it can help you too! The program itself includes Series arithmetic and geometric , Sigma, Pascals triangle, Trig helps, Conic sections, everything having to do with the law of sines and cosines, and to top it all off, a quadratic solver program.
Points to Polynomial 2. This program may crash. I am not responsible for any damage to your calculator. Radians Ultimate Program Pre Calculus program regarding radians 1. Convert Radians to Degrees or Degrees to Radians 2. Pyth Thm 3. Arc and Sector Area 4. Find sinx,cosx,tanx RAM v1. Very useful for all calculus students. Recursive Trapezoid Rule This program uses a recursive version of the trapezoid rule to compute the area under a curve. It is the first column in the Romberg integration technique.
It is a slow program but it can serve as a good example of how recursion works for beginning students in numerical analysis. The user enters in the left endpoint A , the right endpoint B , the function and the number of steps to take in the recursion. The sequence is plotted against its term number in a graph situation , though reading off L2 for the sequence is more handy especially for busy-work.
Related Rates This program works with related rates problems for right triangles and circles. The user inputs the information and the program will output an answer.
Great for first year calculus students. Riemann Sums This program will find the area under a curve, typing in the equation as Y1, and then telling the upper and lower bounds and the number of partitions.
Riemann This program computes left, right, midpoint, and trapezoidal sums for a given function over a given interval. It also draws the rectangular or trapezoidal regions under the graph.
Also included is the definite integral over the region. Great for Numerical Analysts or for Differential equations. The underlying algorithm is an adaptive third-order Runge-Kutta algorithm using coefficients due to Bogacki and Shampine. Please send suggestions, comments, criticism, and bug reports to thornahawk yahoo.
Originally at unitedti. Romberg This program will perform Romberg integration on a function. Please read the description of the program. Great for numerical methods students. Romberg Integration This program will integrate a function between two limits using the Romberg Integration technique. It outputs a 6x6 triangular table with the resluts in lists L1 through L6. Root Finder v. Great for calculus students and teachers for a different problem to give. Riemann Sums This program graphically calculates the Riemann sum of a function, with a customisable number of intervals, and displays it for you.
Riemann Sum v1. This program fixed a small bug and it is now perfect. Rules This program contains all the basics derivative rules for your Calculus 1 and Calculus 2 classes.
This program started by Ryan Heeren as a way to help him remember all the derivative rules. Then I picked it up and improved it. Runge Kutta's Method v1. Same as Improved Euler's method, but more accurate. Runge-Kutta 4 Method Uses the Runge-Kutta 4-slope method to numerically approximate the solutions of first-order differential equations. Derive This file includes two programs for symbolic differentiation and calculation of MacLaurin polynomials. But the hard work is done by the Symbolic and PrettyPrint apps.
Secant Method This program performs the secant method for solving equations. Secant to Tangent This program demonstrates the limit operation of the secant line to the tangent line. The user may need to adjust the window on the program before running it so that tangent lines come in clearly. The user inputs the function, the starting point, A and the initial step size, H. The program generates four secant lines and stores the slopes in L1.
This program is meant to demonstrate the beginnings of the limit process to enhance understanding of the definition of derivative.
Derivative Approximation with Secant Line Slope Gives slope of the secant line through any two points on a function and compares it to the actual derivative. Sequence SEQUENCE is designed to numerically and graphically represent the sequences that result from all types of functions, especially those whose values only carry meaning in the domain of the natural numbers: factorials, series, alternating series, etc. ZoomStat displays the L1,L2 alongside Y1. Shell integration This program will perform shell integration as a method for determining volumes of revolutions as long as the shell is perpendicular to the axis of revolution.
Integral: Shell Method This simple program lets you input a function, enter right and left bounds, and find the volume of the solid by the shell method. Simpson's Rule v1. It estimates areas under curves using this method. It's nice to use it to check your answers, if you are in calculus. In the future I will make a program that also shows all steps. Simpson's Rule Allows you to input the beginning and end of the interval "a" for the start, "b" for the end and the number of subdivisions "n".
When you input the equation, you must be sure to put it in parantheses, otherwise it won't work. Simpson's Rule This program prompts the user for "A" The lower limit of integration , "B" The upper limit of integration , "N" The given number of subintervals , and "Function" The function for which the program will use Simpson's Rule to approximate the integral. The program stores the answer in the variable "X" for reference by the user after the program is finished. Remember the Simpson's Rule is only valid when n is even.
The program will stop if n is odd. Skew Lines This program will inform the user if two lines in space are skew, not skew or parallel. This is the best slope field program out there, simply stated. This program graphs the slope field of a derivative, a technique used in calculus for many purposes. This technique is most useful when trying to integrate a non-integrable function or when integrating a derivative in terms of y or y and x. In addition this version contains Euler's method!
It will numerically integrate a derivative with negligible error if the change in x delta-x is small enough. Simply enter the derivative and watch the program generate the slope field right on the graph screen! In-program options include changing the number of slope lines, adjusting the window, and turning the axes off and on. Slope Field Creator for Calculus This program allows the user to show the slope field plot of a function given the function of its derivative.
Strengths of program: 1 Optimized for speed e. Slope of Secant Line Finds the slope of the secant line when you enter the function, first X point, and change in X. Slope of the tangent This program graphically approximates the slope of the tangent line for a function using the left-right average method.
Slope Field This program calculates a slope field for a given derivative. The slopes can be defined in terms of both y and x. There are also many menus that allow you to customize your slope field. You can set the window and the amount of resolution.
It eats up a ton of memory while you're running it, so you may need to either archive things, or set the resolution to "low". This updated version fixes a minor bug and causes the program to run much faster than before.
It also provides an opportunity to input a solution to the differential equation and view its graph on the slope field. Solids of Revolution calculator Calculate the volume of a solid of revolution automatically.
Great for numerical analysis. Enter function in Y1 and start the program. Enter lower limit, upperlimit and the sub-divisions. It's as easy as that. NB: when you pick ex. Surface Area of Revolution Enter f x , g x , lower bound, upper bound, and then select the axis of revolution and the line to revole around, and it will give you the surface area of revolution.
Survival Function This program will graph the survival function based on hazard rates. Useful for actuarial sciences. Automatic Synthetic Division Solves synthetic division for you by finding factors! You'll be the first one in class to find the solutions! Give it a try, it's only bytes. Also calculates synthetic division manually. Tan between Two Lines Various methods for calculating the tangent of the angle between two intersecting lines.
From there, the program will calculate the equation of the tangent line for that equation and at the entered X value. This program will also store both equations into the Y1 and Y2 variables of the calculator.
Lanczos3 This program computes the third derivative of a function using Lanczos's differentiation by integration formula. Since it is based on least-squares approximations results will not be entirely accurate, but are usually close enough for good approximations. Ticket Prices This program computes the optimal price for ticket sales problems as well as the number expected to attend under this price.
The user inputs the information please read over the description so you know what the values mean. Great for business calculus or applied calculus students. TNB This folder contains four programs for computing the following: 1 components of acceleration, TNB vectors, torsion and TNB planes osculating plane, rectifying plane, normal plane all done at a point.
Great for multivariate calculus or physics students. Total Area This program will compute the total area between a curve and the x-axis.
Trapezoidal Rule This program is for the trapezoidal rule for approximating integrals. Includes approximation, max error, graphs of approximating trapezoids. Trapezoidal Rule v1. Often mentioned in Calculus books in the chapter containing the Trapezoidal Rule.
Trapezoid Approximation of Integrals These problems always annoyed me, so I created a program to do them for me. Trapezoid Rule v1. Simply enter an equation, the lower and upper bounds, and the number of trapezoids; the program will approximate the area under the curve. Great for Calculus students; Doors CS v4.
Trig Anti-Derivative Includes formulas for the derivative and antiderivative for cos, sin, sec, cos Trig Derivatives A simple little program that lists the common derivatives of trig functions.
Triple Integral This program will compute triple integrals using composite Simpson rule. It can run slow, but it is often accurate. Please read documentation.
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