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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 28

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 28

Answers (1)

Answer:

Derivation of sin \; x with respect to cos \; x   is -cot \; x.
Hint:

By using the chain rule of differentiation.

Given:

Derivation of sin \; x with respect to cos \; x   is \cos \; x.
Solution:  

We have to find

\frac{d}{d(\cos x)}(\sin x)

So, we use the chain rule of differentiation to evaluate this.

\frac{d}{d(\cos x)}(\sin x)=\frac{d(\sin x)}{d x} \cdot \frac{d x}{d(\cos x)}

                             \begin{aligned} &=\cos x \cdot \frac{1}{-\sin x} \\\\ &=-\cot x \end{aligned}

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