CBSE Class 12 Mathematics sample paper 2024-25: question 23(b)

Hints

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Step-by-step solution

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1. Let $y=(\cos x{)}^x=e^{x\log \cos x}$. Differentiating, $\frac{dy}{dx}=e^{x\log \cos x}\frac{d}{dx}(x\log \cos x)$.

   ½ mark

2. By the product rule, $\frac{dy}{dx}=(\cos x{)}^x\left\{\log \cos x\cdot 1+x\frac{d}{dx}(\log \cos x)\right\}$.

   ½ mark

3. $=(\cos x{)}^x\left\{\log \cos x+x\cdot \frac{1}{\cos x}(-\sin x)\right\}=(\cos x{)}^x(\log \cos x-x\tan x)$.

   1 mark

Answer: $\frac{dy}{dx}=(\cos x{)}^x(\log \cos x-x\tan x)$

Revise the chapter

• Chapter: Continuity and Differentiability (notes, formulas, where marks are lost and every past question)
• Topic: Logarithmic Differentiation