Definition of Derivative

If y=f(x) is a function of the variable x, then the derivative of y=f(x) at some x=a, is the rate of change of the function with respect to x at a.

The derivative is often interpreted as the slope of the graph of y=f(x) at x=a.

The derivative of y=f(x) is usually written dy/dx or f'(x).

For f(x)=x^3

f'(x)=3x^2, thus the rate of change of x^3 at x=4 is 3×4^2=48.

New! Comments

Have your say about what you just read! Leave me a comment in the box below.

Find a Math Word here

Can't find the word you are looking for? Do a search here and type your word in the box below

Good, better best.

Never, ever rest.

Until your good is better

And your better is your best.

Like this website?

Like it on facebook!

"I am getting much better test marks and I have been moved up a set"
Age 13

"High school's great, I'm in a good math set and I understand lots of things, thanks to you"
Eleanor Talbot
Age 11

"I really like math now, you just make it more friendly and normal"
Jess Johnson
Age 18

"Your writing style is great, informative but friendly! My 12 year old son still struggles with basic maths. I can see your website will be a real treasure trove for us :)"
New Zealand

"My grades have improved and I am doing much better than everyone else in my class"
Age 14

"Thanks for teaching me fractions, You made it so easy kalamuni!"
Abrar Haider
Age 8