Question

Find the derivative of $f\left(x\right)=10x$.

Answer 1

Given : $f\left(x\right)=10x$
We know that $f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}$
$\Rightarrow f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{10(x+h)-10x}{h}$
$\Rightarrow f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{10x+10h-10x}{h}$
$\Rightarrow f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{10h}{h}$
$\Rightarrow f^{\prime }\left(x\right)=10$
Hence, $f^{\prime }\left(x\right)=10$