Question

from the definition of the derivative of a function find f'(x) if y=f(x)=x^2+2

Answer 1

The definition is:
\[\lim_{ \lambda \rightarrow 0}\frac{f(x)-f(x+ \lambda)}{\lambda}\]
So you would have:
\[\lim_{\lambda \rightarrow 0}\frac{x^2+2-((x+\lambda)^2+2)}{\lambda}\]
Foil it out and you should come to the conclusion (after taking the limit) that:
f'(x)=2x

Answer 2

so basically ((x+h)^2+2-(x^2+2))/h then simplify from there. thanks!

Answer 3

Yup :D