Differentiate the following with respect to x:

Question:
Differentiate the following with respect to x:

$\sin x \sin 2 x$

Solution:

To Find: Differentiation

NOTE : When 2 functions are in the product then we used product rule i.e

$\frac{d(u, v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

Let us take y = sin x sin 2x

So, by using the above formula, we have

$\frac{d}{d x}(\sin x \sin 2 x)=\sin x \frac{d(\sin 2 x)}{d x}+\sin 2 x \frac{d(\sin x)}{d x}=\sin x(2 \cos 2 x)+\sin 2 x(\sin x)=$

$2 \sin (x) \cos (2 x)+\sin 2 x(\sin x)$

Differentiation of $y=\sin x \sin 2 x$ is $2 \sin (x) \cos (2 x)+\sin 2 x(\sin x)$