ExamBro
ExamBro
CUET · MATHS · PYQ PAPER 2023

The differential coefficient of \(\log _e\left[\log _e\left(\log _e x^5\right)\right]\) with respect to \(x\) is:

  1. A \(\frac{5}{x \log _e\left(\log _e x^5\right)}\)
  2. B \(\frac{5}{x \log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)
  3. C \(\frac{5 x^4}{\log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)
  4. D \(\frac{5 x}{\log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{5}{x \log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)

Step-by-step Solution

Detailed explanation

\( \frac{d}{dx} \left( \log _e\left[\log _e\left(\log _e x^5\right)\right] \right) = \frac{1}{\log _e\left(\log _e x^5\right)} \cdot \frac{1}{\log _e x^5} \cdot \frac{1}{x^5} \cdot 5x^4 \) \( = \frac{5x^4}{x^5 \log _e x^5 \log _e\left(\log _e x^5\right)} \)…