Question

Differentiate the function w.r.t.x:
(x sin x + cos x)(x cos x - sin x)

Answer 1

HOPE IT HELPS U ✌️✌️✌️

Answer 2

To find the differentiation of the given function we have to apply UV formula of differentiation

$\frac{d(UV)}{dx} = U \frac{dV}{dx} + V\frac{dU}{dx} \\ \\ \frac{d(x \: sin \: x + cos \: x)(x \: cos \: x - sin \: x)}{dx} \\ \\ = (x \: sin \: x + cos \: x) \frac{d(x \: cos \: x - sin \: x)}{dx} + (x \: cos \: x - sin \: x)\frac{d(x \: sin \: x + cos \: x)}{dx} \\ \\ = (x \: sinx + cos \: x)( - x \: sin \: x + cos \: x - cos \: x) + (x \: cos \: x - sin \: x)(x \: cos \: x + sin \: x - sin \: x) \\ \\ = (x \: sinx + cos \: x)( - x \: sin \: x ) + (x \: cos \: x - sin \: x)(x \: cos \: x) \\ \\ = - {x}^{2} {sin}^{2} x - x \: sin \: x \: cos \: x + {x}^{2} {cos}^{2} x - x \: cos \: x \: sin \: x \\ \\ = {x}^{2} ( {cos}^{2}x - {sin}^{2}x) - 2x \: sin \: x \: cos \: x \\ \\ = {x}^{2} cos \: 2x - 2x \: sin \: x \: cos \: x$
Hope it helps you.