CBSE Class 12 Mathematics 2024: question 27(b)

Hints

Open one hint at a time and try again before the next.

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: $\log y=x\log (\tan x)$

   ½ mark

2. Differentiating w.r.t. $x$ (product rule): $\frac{1}{y}\frac{dy}{dx}=x\cdot \frac{{\sec }^{2}x}{\tan x}+\log (\tan x)\cdot 1$

   2 marks

3. $\frac{dy}{dx}=(\tan x{)}^x\left[\frac{x{\sec }^{2}x}{\tan x}+\log (\tan x)\right]$ (equivalently $(\tan x{)}^x\left[2x\mathrm{cosec}2x+\log \tan x\right]$)

   ½ mark

Answer: $\frac{dy}{dx}=(\tan x{)}^x\left[\frac{x{\sec }^{2}x}{\tan x}+\log (\tan x)\right]$

Revise the chapter

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