Differential coefficient of $log_e[log_e

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

Differential coefficient of $log_e[log_e(log_ex^5)]$ with respect to x is :

Options:

$\frac{5}{xlog_e(log_ex^5)}$

$\frac{5}{xlog_e(x^5)log_e(log_ex^5)}$

$\frac{5x^4}{log_e(x^5)log_e(log_ex^5)}$

$\frac{5x}{log_e(x^5)log_e(log_ex^5)}$

Correct Answer:

$\frac{5}{xlog_e(x^5)log_e(log_ex^5)}$

Explanation:

The correct answer is Option (2) → $\frac{5}{xlog_e(x^5)log_e(log_ex^5)}$

$y=\log\log\log x^5$

$\frac{dy}{dx}=\frac{5x^4}{x^5(\log(\log x^5))(\log x^5)}$

Using chain rule

$=\frac{5}{x(\log(\log x^5))(\log x^5)}$