Home/
Competitive Exams/
JEE Main & Advanced/
Mathematics/
Differentiability/
Question 360005
JEE Mathematics · Medium

Differentiability: Logarithmic differentiation MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

Timer-based practiceDetailed answer reviewMobile-friendly flow
Logarithmic differentiationMediumQuestion 360005

Question

To differentiate y = xˢⁱⁿ ˣ, we use:
  1. A
    Logarithmic differentiation: take ln, then differentiate
    Correct
  2. B
    Power rule directly
  3. C
    Chain rule only
  4. D
    Product rule directly

Correct answer

Logarithmic differentiation: take ln, then differentiate

Explanation

For y = f(x)^g(x), take ln: ln y = g(x) ln f(x). Differentiate both sides: y'/y = g'(x) ln f(x) + g(x) f'(x)/f(x). Multiply by y for y'.

Review Differentiability notesStart timed chapter practice