Question

Find the derivative of $sin\left[co{s}^2\right(x{)}^3]$ w.r.t $x$

Answer 1

Let $y=sin\left[co{s}^2{x}^3\right]$

Differentiate on both sides w.r.t x

$\frac{dy}{dx}=\frac{d}{dx}\left(sin\right(co{s}^2\left(x^3\right)\left)\right)$

$=cos\left(co{s}^2\right(x^3\left)\right)\ast \frac{d}{dx}\left(co{s}^2\right(x^3\left)\right)$

$=-2cos\left(co{s}^2\right(x^3\left)\right)sin{x}^{3}cos{x}^3\frac{d}{dx}\left(x^3\right)$

$\therefore \frac{dy}{dx}=-3x^{2}sin\left(2x^3\right)cos\left(co{s}^2\right(x^3\left)\right)$