Question

$y=cos{x}^3,then\frac{dy}{dx}$=?

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is D

none of these

These type of questions are done by substitution.
Put $x^3=u$, differentiating u w.r.t. 'x'
$\therefore 3x^2=\frac{du}{dx}.....\left(i\right)$
Also y=cos u
Now differentiating y w.r.t. u,$\frac{dy}{du}=-sinu=-sin{x}^3$....(ii)

Using (i) and (ii) $\frac{dy}{du}.\frac{du}{dx}=\frac{dy}{dx}=-3x^{2}sin{x}^3$