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