Find the derivative of the following functions using [f(x+h) – f(x)]/h

Question

LIM h-0
ƒ(x) = x^2 + 5^x
ƒ(x)= 1/2^x
Show all your steps.

I've been stuck on this question for a while,I understand how to do just the 5^x but not with the x^2 also. Any help appreciated, thanks.

Answer 1

d/dx (x^2)?

f(x+h) = (x+h)^2 = x^2 + 2 h x + h^2
f(x) =x^2

f(x+h) - f(x) = 2 h x + h^2
divide by h
2 x + h
let h --> 0
2x