Differentiate the following with respect to x:

To Find: Differentiation

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

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

Formula used: $\frac{d}{d x} \sin ^{2}(a x+b)=2 \sin (a x+b) \frac{d}{d x} \sin (a x+b) \frac{d}{d x}(a x+b)$

Let us take $y=\sin ^{2}(2 x+3)$

So, by using above formula, we have

$\frac{d}{d x} \sin ^{2}(2 x+3)=2 \sin (2 x+3) \frac{d}{d x} \sin (2 x+3) \frac{d}{d x}(2 x+3)=4 \sin (2 x+3) \cos (2 x+3)$

Differentiation of $y=\sin ^{2}(2 x+3)$ is $4 \sin (2 x+3) \cos (2 x+3)$