Question

Differentiate log⁡(log⁡x^5) w.r.t x.

(a) –\(\frac{5}{x log⁡x^5}\)

(b) \(\frac{1}{log⁡x^5}\)

(c) \(\frac{5}{x log⁡x^5}\)

(d) –\(\frac{1}{x log⁡x^5}\)

This question was posed to me during an interview.

I want to ask this question from Exponential and Logarithmic Functions in section Continuity and Differentiability of Mathematics – Class 12

Answer 1

Correct option is (c) \(\frac{5}{x log⁡x^5}\)

The best explanation: Consider y=(log⁡(log⁡(x^5)))

\(\frac{dy}{dx}=\frac{1}{log⁡x^5} \frac{d}{dx} (log⁡x^5)\)

\(\frac{dy}{dx}=\frac{1}{log⁡x^5}.\frac{1}{x^5}.\frac{d}{dx} (x^5)\)

\(\frac{dy}{dx}=\frac{1}{log⁡x^5}.\frac{1}{x^5}.5x^4\)

∴\(\frac{dy}{dx}=\frac{5}{x log⁡x^5}\)