# Thread: Differentiate from first principles?

1. ## Differentiate from first principles?

Q1) Given that f(x) = 2x^3 + x , find ;
(a) the derivative of f(x) with respect to x, from first principles

can somebody explain the answers that are given here (pdf file) and it is question 1 on the exam paper, and also what exactly is the difference between first principles and regular differentiation? Thanks A LOT!

2. Hello
Originally Posted by scott_237
Q1) Given that f(x) = 2x^3 + x , find ;
(a) the derivative of f(x) with respect to x, from first principles

can somebody explain the answers that are given here
What is not clear in this answer?

What exactly is the difference between first principles and regular differentiation?
Finding $f'$ from first principles means using the definition of the derivative : $f'(x)=\lim_{h\to0}\tfrac{f(x+h)-f(x)}{h}$. If you had been allowed to use "regular differentiation" you could have used results which are derived from the definition of the derivative. (for example $(x^n)'=nx^{n-1}$)