CBSE Class 12 Mathematics 2024: question 26(a)

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Taking log on both sides: $y\log \cos x=x\log \cos y$.

   1 mark

2. Differentiating w.r.t. x: $\frac{dy}{dx}\log \cos x+y\cdot \frac{-\sin x}{\cos x}=\log \cos y+x\cdot \frac{-\sin y}{\cos y}\frac{dy}{dx}$, i.e. $\frac{dy}{dx}\log \cos x-y\tan x=\log \cos y-x\tan y\frac{dy}{dx}$.

   1½ marks

3. $\frac{dy}{dx}(\log \cos x+x\tan y)=\log \cos y+y\tan x\Rightarrow \frac{dy}{dx}=\frac{\log \cos y+y\tan x}{\log \cos x+x\tan y}$.

   ½ mark

Answer: $\frac{dy}{dx}=\frac{\log \cos y+y\tan x}{\log \cos x+x\tan y}$

Revise the chapter

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