If f(x) = loga loga(x), then f'(x) is :

CUET Preparation Today

Start Free Mocks

Home Questions 6V6P63TW6A

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

If f(x) = log_a log_a(x), then f'(x) is :

Options:

$\frac{\log _a e}{x \log _e x}$

$\frac{\log _e a}{x \log _a x}$

$\frac{\log _e a}{x}$

$\frac{x}{\log _e a}$

Correct Answer:

$\frac{\log _a e}{x \log _e x}$

Explanation:

$f'(x)=\frac{1}{\log _a x} .\left(\log _a e\right) . \frac{d}{d x}\left(\log _a x\right)$

$=\frac{\log _a e}{\log _a x} . \frac{1}{x} . \log _a e=\frac{\log _a e}{x} . \frac{\log _a e}{\log _a x}=\frac{\log _a e}{x \log _e x}$

Hence (1) is correct answer.