Question

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

Answer 1

`f'(x)=2x+1`

Explanation:

`lim_(hrarr0)[[(x+h)^2+x+h]-[x^2+x]]/h`

`lim_(hrarr0)[[x^2+2xh+h^2+x+h]-[x^2+x]]/h`

`lim_(hrarr0)[x^2+2xh+h^2+x+h-x^2-x]/h`

`lim_(hrarr0)[2xh+h^2+h]/h`

`lim_(hrarr0)[h(2x+h+1)]/h`

`lim_(hrarr0)2x+h+1=2x+0+1=2x+1`