Question

Find the derivative of $\sin 2x$ at $x=\frac{\pi }{3}$ from definition.

Answer 1

We have,

$y=\sin 2x$

On differentiation and we get,

$\frac{dy}{dx}=\cos 2x\left(2\right)$

$\frac{dy}{dx}=2\cos 2x$

At the point $x=\frac{\pi }{3}$

$\frac{dy}{dx}=2\cos \left(\frac{2\pi }{3}\right)$

$\frac{dy}{dx}=2\cos (\pi -\frac{\pi }{3})$

$\frac{dy}{dx}=-2\cos \frac{\pi }{3}$

$\frac{dy}{dx}=-2\times \frac{1}{2}$

$\frac{dy}{dx}=-1$

Hence, this is the answer