Question

Find the derivative of $x^2$ by first principle

Answer 1

$f\left(x\right)=x^2$

First principle

${lim}_{h\to 0}\frac{f(x+h)-f\left(x\right)}{h}{lim}_{h\to 0}\frac{(x+h{)}^2-x^2}{h}{lim}_{h\to 0}\frac{x^2+2xh+h^2-x^2}{h}{lim}_{h\to 0}\frac{h(2x+h)}{h}{lim}_{h\to 0}2x+h=2x$