Question

Derivate $e^{\sqrt{2x+1}}$ where $x=12$ w.r.t. x

Answer 1

Consider the given function.

$y=e^{\sqrt{2x+1}}$

On differentiating both sides w.r.t $x$, we get

$y=e^{\sqrt{2x+1}}$

$\frac{dy}{dx}=e^{\sqrt{2x+1}}\times (\frac{1}{2\sqrt{2x+1}}\times 2)$

$\frac{dy}{dx}=\left(\frac{e^{\sqrt{2x+1}}}{\sqrt{2x+1}}\right)$

On putting $x=12$, we get

${\frac{dy}{dx}|}_{x=12}=\left(\frac{e^{\sqrt{24+1}}}{\sqrt{24+1}}\right)$

${\frac{dy}{dx}|}_{x=12}=\left(\frac{e^{\sqrt{25}}}{\sqrt{25}}\right)$

${\frac{dy}{dx}|}_{x=12}=\frac{e^5}{5}$

Hence, this is the answer.