I'm working on this question:

if f(x) = x^3, then the derivative is 3x^2

I have to prove this using the definition of the derivative. I got as far as this:

I'm unsure of how to simplify it in order to find the limit as h -> 0.

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- June 10th 2010, 07:55 PMGlitchFinding a derivative using first principles
I'm working on this question:

if f(x) = x^3, then the derivative is 3x^2

I have to prove this using the definition of the derivative. I got as far as this:

I'm unsure of how to simplify it in order to find the limit as h -> 0. - June 10th 2010, 08:18 PMStudyBug10
lim h --> 0 of x^3 = [(x+h)^3 - x^3]/h

= [(x+h)(x+h)(x+h) - x^3]/h

= [x^3 + x^2 h + 2 x^2 h + 2 x h^2 + x h^2 + h^3 - x^3]/h

cancel the x^3 and the h's with the one in the bottom

= x^2 + 2 x^2 + 2 x h + x h + h^2

plug in 0 for h

= x^2 + 2 x^2

combine like terms

= 3 x^2

I hope that helps :D - June 10th 2010, 08:31 PMGlitch
Ahh, thanks! The problem was with my simplification of (x+h)^2

- June 10th 2010, 09:33 PMGlitch
I have a similar question:

Find the derivative of using first principles. Once again, I'm having trouble simplifying. :/

I keep getting when it should be - June 10th 2010, 10:16 PMmr fantastic
- June 10th 2010, 10:30 PMGlitch
Working:

As h -> 0,

Which is incorrect. - June 10th 2010, 10:34 PMmr fantastic