Question

Solve : $\frac{d}{dx}\sqrt{1-x^2}$

• A. $\frac{2x}{\sqrt{1-x^2}}$
• B. $\frac{-2x}{\sqrt{1-x^2}}$
• C. $\frac{x}{\sqrt{}1-x^2}$
• D. $\frac{-x}{\sqrt{1-x^2}}$

Answer 1

The correct option is D $\frac{-x}{\sqrt{1-x^2}}$

Let $1-x^2=y$

Now, using Chain rule,

$\frac{d}{dx}\sqrt{y}=\frac{1}{2\sqrt{y}}\times \frac{dy}{dx}$

$=\frac{1}{2\sqrt{1-x^2}}\times \frac{d}{dx}(1-x^2)$

$=\frac{-2x}{2\sqrt{1-x^2}}$

$=\frac{-x}{\sqrt{1-x^2}}$