MHT CET · Maths · Differentiation
If \(u=\cos ^3 x, v=\sin ^3 x\), then \(\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}}\) is equal to
- A -2
- B 2
- C 1
- D -1
Answer & Solution
Correct Answer
(D) -1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & u=\cos ^3 x, v=\sin ^3 x \\ & \therefore \frac{d u}{d x}=3 \cos ^2 x(-\sin x) \text { and } \frac{d v}{d x}=3 \sin ^2 x(\cos x) \\ & \therefore \frac{d v}{d u}=\frac{3 \sin ^2 x \cos x}{-3 \sin x \cos ^2 x}=-\tan x \\ & \therefore\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}}=-\tan \left(\frac{\pi}{4}=-1\right)\end{aligned}\)
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