Consider the terms separately

Hints for f(x) = 2 x^2

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

[f(x+h) - f(x)]/h = 2[ (x+h)^2 -x^2]/h = 2[(x+h-x)(x+h+x)]/h

= 2h(2x+h)/h = 2(2x+h)

What happens as h ->0 ?

f(x) = x^3 f(x+h) = (x+h)^3

[f(x+h)- f(x)]/h = (x+h-x)[(x+h)^2 +(x+h)x + x^2]/h

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

What happens as h -> 0