Derivatives Help

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bCalc

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scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Select precision* of answer:

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Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

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Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90° or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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A derivative is nothing more than a slope. The derivative of a function is a function that represents the slope of the original function for every point throughout its entire domain.

Derivatives can be shown in several different ways: `(dy)/(dx)` = `(d(f(x)))/dx` = `f'(x)`

Let us start with a function that is a constant, for example: `f(x)=5`. We know that this function would be a horizontal line passing through `y = 5`. We also know that the slope of a horizontal line is zero.

Our first formula: If `f(x)=c`, `f'(x)=0` where `c` is a constant.

Let us try a function that has a constant slope, such as: `f(x)=4x`. We know that this function would have a slope of four.

Our second formula: If `f(x)=c*x`, `f'(x)=c`.

Not all derivatives are this easy to find, so you may want to memorize the list of derivatives shown below. If you would like to visualize each function and its derivative, try graphing both using the graphing calculator at the left.

`d/(dx)c = 0` `d/(dx)sin(x)=cos(x)`

`d/(dx)cx = c` `d/(dx)cos(x)=-sin(x)`

`d/(dx)x^c = cx^c-1` `d/(dx)tan(x)=sec^2(x)`

`d/(dx)sqrt(x) = 1/(2sqrt(x))` `d/(dx)cot(x)=-csc^2(x)`

`d/(dx)1/x = -1/x^2` `d/(dx)sec(x)=sec(x)tan(x)`

`d/(dx)ln(x) = 1/x` `d/(dx)csc(x)=-csc(x)cot(x)`

`d/(dx)e^x = e^x` `d/(dx)sin^(-1)(x)=1/sqrt(1-x^2)`

`d/(dx)cos^(-1)(x)=-1/sqrt(1-x^2)`

`d/(dx)tan^(-1)(x)=1/(1+x^2)`