Question

UPLE 3 Differentiate sin 3x cos 5x w.r.t. x.​

Answer 1

Step-by-step explanation:

We have,

$y = \sin(3x) \cos(5x)$

Differentiating both sides,

$= > y = \frac{1}{2} \times 2 \sin(3x) \cos(5x)$

$= > y = \frac{1}{2}( \sin(8x) - \sin(2x) )$

Differentiating both sides,

$= > \frac{dy}{dx} = \frac{d}{dx} ( \frac{ \sin(8x) }{2} - \frac{ \sin(2x) }{2} )$

$= > \frac{dy}{dx} = \frac{8 \cos(8x)}{2} - \frac{2 \cos(2x) }{2}$

$= > \frac{dy}{dx} = 4 \cos(8x) - \cos(2x)$