Q. The derivative of $\sin{(x^{3})}$ w.r.t.$\cos\left( x^{3} \right)$ is
A) $- tan(x^{3})$
B) $tan(x^{3})$
C) $- cot(x^{3})$
D) $cot(x^{3})$
Explanation
(c)
Let $u = \sin x^{3}\ and\ v = \cos x^{3}$.
On differentiating w.r.t. $x,\$we get
$\frac{du}{dx} = \cos{x^{3}.3x^{2}\ and\frac{dv}{dx} = - \sin{x^{3}.3x^{2}}}$
$\therefore\frac{du}{dv} = \frac{du/dx}{dv/dx} = \frac{3x^{2\ }\cos x^{3}}{- 3x^{2}\sin x^{3}} = - \cot x^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.