Question

Differentiate the function 𝑓(𝑥) = 5𝑥 2 + 2 using the first principle

Answer 1

$$f'(x)=\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}$$

$$=\lim\limits_{h\to 0}\dfrac{5(x+h)^2+2-(5x^2+2)}{h}$$

$$=\lim\limits_{h\to 0}\dfrac{5x^2+10xh+5h^2+2-5x^2-2}{h}$$

$$=\lim\limits_{h\to 0}(10x+5h)=10x+0=10x$$

$$f'(x)=(5x^2+2)' =10x$$