Differentiation from First Principles

Question 1

As ‘h’ tends towards 0, what does (f(x+h)-f(x))/h) tend towards?

Answer 1

f’(x)

Question 2

What is the derivative of f(x)?

Answer 2

lim h -> 0 (f(x+h)-f(x))/h

Question 3

What should not be left out of each step?

Answer 3

lim h -> 0

Question 4

h is NEVER =

Answer 4

to 0

Question 5

What finishing statements should you ALWAYS put at the end of a differentiation from 1st principles e.g prove from 1st principles of differentiation that the derivative of 3x^2 is 6x

Answer 5

h–>0
3h–>
so f’(x)–>6x