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Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Fill in the blanks question  20 maths

Answers (1)

Answer: \text { tan } u

Hint: \text { put } u=\cos x \text { and } v=\sin x

Given: The derivative of \cos \; x  w.r.t \sin x

Solution:  

\begin{aligned} &\text { Let } u=\cos x \text { and } v=\sin x \\\\ &\frac{d u}{d v}=-\sin x &\frac{d v}{d u}=\cos x \end{aligned}

Therefore:

\begin{aligned} &\frac{d u}{d v}=\frac{d u \mid d v}{d v \mid d u}=\frac{-\sin x}{\cos x} \\\\ &=-\tan x \end{aligned}

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