# How do you find f'(x) using the definition of a derivative for #f(x)=x^3 + 2x^2 + 1#?

##### 1 Answer

Oct 17, 2015

The derivative is

#### Explanation:

The definition is:

So the terms are:

Term by term, we have:

#(x+h)^3=x^3+3 x^2 h+3 x h^2+h^3# #2(x+h)^2 = 2(x^2+2hx+h^2)=2x^2+4hx+2h^2#

Obviously,

Now we compute

Now we divide this quantity by

Now, taking the limit of this quantity as