# Thread: derivative of a function

1. ## derivative of a function

Hello, I have finals over a few calculus concepts covered in pre-calc class in a couple of days. Here is a problem I would like solved with the written step by step process. Not trying to cheat or anything i just want to have the step by step process so it is clearer in my mind, especially since i need a decent score on the test. thx.

1. Find the derivative of f(x)=x^3

2. Originally Posted by thermisius
Hello, I have finals over a few calculus concepts covered in pre-calc class in a couple of days. Here is a problem I would like solved with the written step by step process. Not trying to cheat or anything i just want to have the step by step process so it is clearer in my mind, especially since i need a decent score on the test. thx.

1. Find the derivative of f(x)=x^3
Calculate $\displaystyle \frac{f(x+h)-f(x)}h$ and take the limit as $\displaystyle h\to0.$

$\displaystyle \frac{f(x+h)-f(x)}h=\frac{(x+h)^3-x^3}h=\frac{3x^2h+3xh^2+h^3}h=3x^2+3xh+h^2$

Hence the limit as $\displaystyle h\to0$ is $\displaystyle 3x^2.$

3. thank you, that really helps me out.