What is the derivative of [(x)^(5/3)] and [(x)^(4/3)] using the long method ?

Question

The "long method" that I'm saying is:
f(x) = [(x)^(5/3)]
f(x + h) = ?
f(x + h) - f(x) = ?
[f(x + h) - f(x)] / h = ?
limit of {[f(x + h) - f(x)] / h} as h approaches 0 = ?

f(x) = [(x)^(4/3)]
f(x + h) = ?
f(x + h) - f(x) = ?
[f(x + h) - f(x)] / h = ?
limit of {[f(x + h) - f(x)] / h} as h approaches 0 = ?

Answer 1

Why use the long method?

The answers are:

1. F'(x) = 5/3x^2/3

2. F'(x) = 4/3x^1/3

Answer 2

You must really want the answer as you put this on twice.