Question

Differentiate the function w.r.t.x:
x⁴ (5 sin x - 3 cos x)

Answer 1

HOPE IT HELPS U ✌️✌️

Answer 2

To differentiate the given function,we have to apply UV rule of differentiation

$\frac{d(UV)}{dx} = U \frac{dV}{dx} + V\frac{dU}{dx} \\ \\ here \: let \: U = {x}^{4} \\ \\ V = 5sin \: x - 3cos \: x$
and we know that
$\frac{d {x}^{n} }{dx} = n {x}^{n - 1} \\ \\ \frac{d \: cos \: x}{dx} = - sin \: x \\ \\ \frac{d \: sin \: x}{dx} = cos \: x$
$\frac{d( {x}^{4})(5sin \: x - 3cos \: x)}{dx} = {x}^{4} \bigg(\frac{d(5sin \: x - 3cos \: x)}{dx}\bigg) + (5sin \: x - 3cos \: x)\bigg(\frac{d {x}^{4} }{dx}\bigg)\\ \\ = {x}^{4}(5cos\: x + 3sin \: x) + (5sin \: x - 3cos \: x)(3 {x}^{3} ) \\ \\ = {x}^{4}(5cos\: x + 3sin \: x) + 3 {x}^{3} (5sin \: x - 3cos \: x)$
Hope it helps you.