Question

If $y=\sin 4x$, then find $\frac{dy}{dx}$ at $x=\frac{\pi }{4}$.

Answer 1

We have,

$y=\sin 4x$

$\frac{dy}{dx}=4\cos 4x$

Since, $x=\frac{\pi }{4}$

Therefore,

$\Rightarrow \frac{dy}{dx}{|}_{x=\frac{\pi }{4}}=4\cos \frac{\pi }{4}$

$=4\times \frac{1}{\sqrt{2}}$

$=4\times \frac{1}{\sqrt{2}}$

$=2\sqrt{2}$

Hence, this is the answer.