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

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

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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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