If $y=\log \left(\frac{1-x^2}{1+x^2}\rig

CUET Preparation Today

Start Free Mocks

Home Questions GKQVAQRFBX

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Continuity and Differentiability

Question:

If $y=\log \left(\frac{1-x^2}{1+x^2}\right)$, then $\frac{d y}{d x}$ is :

Options:

$\frac{-4 x^3}{1-x^4}$

$\frac{4}{1-x^4}$

$\frac{-4 x}{1-x^4}$

$\frac{4 x^3}{1-x^4}$

Correct Answer:

$\frac{-4 x}{1-x^4}$

Explanation:

$y=\log \left(1-x^2\right)-\log \left(1+x^2\right)$

$\Rightarrow \frac{d y}{d x}=\frac{-2 x}{1-x^2}-\frac{2 x}{1+x^2}=\frac{-4 x}{1-x^4}$

Hence (1) is correct answer.