Example first principles differentiation

Find these derivatives by FIRST PRINCIPLES, meaning that if $y=f(x)$ then

$$f'(x)=\displaystyle\lim_{h\rightarrow 0} \dfrac{f(x+h)-f(x)}{h}$$

Please Note: You only do the derivative this way when the question says to do it by FIRST PRINCIPLES, and otherwise you use formulas.