Question

Using the definition of a derivative how do you calculate the derivative of `f(x) = x^2 + x`?

Answer 1

`lim_{h->0}(f(x+h)-f(x))/h=lim_{h->0}((x+h)^2+(x+h)-x^2-x)/h`

`=lim_{h->0}(x^2+2xh+h^2+h-x^2)/h=lim_{h->0}(h(2x+h+1))/h`

`=lim_{h->0}(2x+1+h)=2x+1`.