Q100 / 150 · MHT CET 2009 · Mathematics

The derivative of $\cos ^{3} x$ w.r.t. $\sin ^{3} x$ is

  • Correct answer
    A
    $-\cot x$
  • B
    $\cot x$
  • C
    $\tan x$
  • D
    $-\tan x$

Solution

Let $\begin{aligned} u=\cos ^{3} x, v=\sin ^{3} x \\ \frac{d u}{d x}=-3 & \cos ^{2} x \sin x, \frac{d v}{d x}=3 \sin ^{2} x \cos x \\ \text { Now, } \frac{d u}{d v} &=\frac{-3 \cos ^{2} x \sin x}{3 \sin ^{2} x \cos x} \\ &=-\frac{\cos x}{\sin x} \\ &=-\cot x \end{aligned}$

Hence, the correct answer is option: 'A'.

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