Derivative Plotter

Have fun with derivatives!
Type in a function and see its slope below (as calculated by the program).
Then see if you can figure out the derivative yourself.

images/function-graph-deriv.js

It plots your function in blue, and plots the slope of the function on the graph below in red (by calculating the difference between each point in the original function, so it doesn't know the formula for the derivative).

You also have the option to plot another function in green beneath that calculated slope ... if the lines coincide there's a good chance you have found the derivative!

Your Turn:

Type x^2 into the blue function box at the top
Look at the red line in the bottom graph ... it shows the slope. Notice it is a straight line
Now, try to match that red line. Type a guess in the bottom box (like x, 2x, or 3x)
When your green line perfectly matches the red line, you have found the derivative

Things To Try

See if you can find the derivative by trying different functions at the bottom.

"Powers":

function:	x	x²	x³	x⁴	x⁵
derivative:	1	?x	?x²	?...	?...
See if you can discover the pattern!

(Note the plotter prefers x² entered as x^2, x³ as x^3 and so on)

Trigonometry Functions:

function:	sin(x)	cos(x)	tan(x)
derivative:	cos(x)	?	?

Exponential Functions:

function:	e^x	ln(x)
derivative:	?	?

Try entering e^x in the top box. What do you notice about the red slope graph compared to the blue function graph? They are exactly the same! The derivative of e^x is itself!

How Did You Go?

Ready to see if your guesses are correct? Check out the Derivative Rules page to see the formal formulas.

Cautions:

This is just a numerical estimate, it does not know the formula for the derivative ... that's up to you to find!

Also, because it just does simple calculations, it won't handle special conditions such as holes, jumps, and so on. See Continuity.

But it is a fun and educational tool, so enjoy!