Question

Differentiate w.r.t. $x$:

$y=\left(\cos x\right)(1-{\sin }^{2}x)$

Answer 1

$y=\left(\cos x\right)(1-{\sin }^{2}x)$

$y=\cos x\times {\cos }^{2}x$

$y={\cos }^{3}x$

Differentiating w.r.t x, we get,

$\frac{dy}{dx}=3{\cos }^{2}x\times (-\sin x)$

$\frac{dy}{dx}=-3\sin x{\cos }^{2}x$