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