Question

Find the differentiation by chain rule : [sin (4x +9)]²​...answer seems to be sec x²(2x)​
Plz full solution

Answer 1

Hi.

This is rewritable as:

$[sin(4x+9)]^2=sin^2(4x+9)$

Now differentiate in order:

Square → sin → bracket i.e (4x+9)

$\frac{d}{dx}sin^2(4x+9)\\2sin(4x+9)*\frac{d}{dx}sin(4x+9)\\2sin(4x+9)*cos(4x+9)*\frac{d}{dx}(4x+9)\\2sin(4x+9)*cos(4x+9)*4\\8sin(4x+9)*cos(4x+9)$