Question

Another question,
if f(x+h)-f(x)= -3hx**2+4hx-8h**2x+5h**2-3h**3,
what is f'(x)?

Answer 1

Looks like you are learning derivatives from First Principles.

By definition,
f'(x) = limit [(f(x+h)-f(x))/h] as h --> 0

you were given the f(x+h)-f(x) part as
-3hx^2 + 4hx - (8h^2)x + 5h^2 - 3h^3 , (I read your ** as exponents)

so f'(x)
= limit(-3hx^2 + 4hx - (8h^2)x + 5h^2 - 3h^3)/h as h---0
= limit (-3x^2 + 4x - (8h)x + 5h - 3h^2 as h ---> 0
= -3x^2 + 4x