MHT CET · Maths · Differentiation
The derivative of \(\cos ^{3} x\) w.r.t. \(\sin ^{3} x\) is
- A \(-\cot x\)
- B \(\cot x\)
- C \(\tan x\)
- D \(-\tan x\)
Answer & Solution
Correct Answer
(A) \(-\cot x\)
Step-by-step Solution
Detailed explanation
Let
\(u=\cos ^{3} x, v=\sin ^{3} x \)
\( \frac{d u}{d x}=-3 \cos ^{2} x \sin x, \frac{d v}{d x}=3 \sin ^{2} x \cos x \)
\( \text { Now, } \frac{d u}{d v} =\frac{-3 \cos ^{2} x \sin x}{3 \sin ^{2} x \cos x} \)
\( =-\frac{\cos x}{\sin x} \)
\(=-\cot x\)
\(u=\cos ^{3} x, v=\sin ^{3} x \)
\( \frac{d u}{d x}=-3 \cos ^{2} x \sin x, \frac{d v}{d x}=3 \sin ^{2} x \cos x \)
\( \text { Now, } \frac{d u}{d v} =\frac{-3 \cos ^{2} x \sin x}{3 \sin ^{2} x \cos x} \)
\( =-\frac{\cos x}{\sin x} \)
\(=-\cot x\)
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