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:
- A \(\frac{5}{x \log _e\left(\log _e x^5\right)}\)
- B \(\frac{5}{x \log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)
- C \(\frac{5 x^4}{\log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)
- D \(\frac{5 x}{\log _e\left(x^5\right) \log _e\left(\log _e x^5\right)}\)
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
\( \frac{d}{dx} \left( \log _e\left[\log _e\left(\log _e x^5\right)\right] \right) = \frac{1}{\log _e\left(\log _e x^5\right)} \cdot \frac{1}{\log _e x^5} \cdot \frac{1}{x^5} \cdot 5x^4 \) \( = \frac{5x^4}{x^5 \log _e x^5 \log _e\left(\log _e x^5\right)} \)…
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