Let $y=\log _x 5$, then $\frac{d y}{d x}

CUET Preparation Today

Start Free Mocks

Home Questions GQT7UKGDDC

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

Let $y=\log _x 5$, then $\frac{d y}{d x}=$

Options:

$\frac{\log 5}{x(\log x)^2}$

$\frac{-\log 5}{x(\log x)^2}$

$\frac{-\log 5}{(\log x)^2}$

$\frac{\log 5}{x}$

Correct Answer:

$\frac{-\log 5}{x(\log x)^2}$

Explanation:

The correct answer is Option (2) - $\frac{-\log 5}{x(\log x)^2}$

$y=\log _x 5=\frac{\log 5}{\log x}$

$\frac{dy}{dx}=\frac{-\log 5}{(\log x)^2}×\frac{1}{x}$