Question

Find the derivative by first principle in examples to $\left(8\right)$
$3x^2+4$

Answer 1

Let $f\left(x\right)=3x^2+4$

$f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}=\underset{h\to 0}{lim}\frac{3(x+h{)}^2+4-3x^2-4}{h}=\underset{h\to 0}{lim}\frac{3(x+h+x)(x+h-x)}{h}=\underset{h\to 0}{lim}3(2x+h)=6x$