Question

derivative of x^2 sin x divided by cos x​

Answer 1

Answer:

$\frac{d}{dx} \: ( {x}^{2} \frac{ \sin(x) }{ \cos(x) } ) \\ \\ = \frac{d}{dx} ( {x}^{2} \: \tan \: x ) \\ \\ = {x}^{2} \frac{d}{dx} (tan \: x) + tan \: x \: . \: \frac{d}{dx} {x}^{2} \\ \\ = {x}^{2} {sec}^{2} x + tan \: x.2x \\ \\ = x(x. {sec}^{2} x + 2tan \: x)$

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Formula used :-

d/dx (u.v)

= u. d/dx(v) + v. d/dx(u)