Question

If the derivative of the function $4\sqrt{x}-2$ is $\frac{a}{\sqrt{x}}.$ Find the value of $a$.

Answer 1

Let $f\left(x\right)=4\sqrt{x}-2$
$f^{\prime }\left(x\right)=\frac{d}{dx}(4\sqrt{x}-2)=\frac{d}{dx}\left(4\sqrt{x}\right)-\frac{d}{dx}\left(2\right)$
$=4\frac{d}{dx}\left(x^{\frac{1}{2}}\right)-0=4\left(\frac{1}{2}{x}^{\frac{1}{2}-1}\right)$
$=\left(2x^{-\frac{1}{2}}\right)=\frac{2}{\sqrt{x}}$