Question

Find the derivative :$\sin 2x$

Answer 1

Here, we know that chain rule is,

$\frac{d}{dx}(f\left(g\left(x\right)\right)=\frac{d}{d\left(g\left(x\right)\right)}(f\left(g\left(x\right)\right)\cdot \frac{d}{dx}\left(g\left(x\right)\right)$

Now using it on the given derivative we get,

$\frac{d}{dx}\left(\sin \left(2x\right)\right)=\frac{d}{d\left(2x\right)}\left(\sin \left(2x\right)\right)\cdot \frac{d}{dx}\left(2x\right)=\cos \left(2x\right)\cdot 2=2\cos \left(2x\right).$