If f(x)=1-x^2, x (0,1), then f^ (x), is equal to - Vidyadip

MCQ

If $f(x)=\sqrt{1-x^2}, x \in(0,1)$, then $f^{\prime}(x)$, is equal to

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

✓

Answer

(d) $\frac{-x}{\sqrt{1-x^2}}$
Explanation: $f ( x )=\sqrt{1-x^2}$
$f^{\prime}(x)=\frac{1}{2 \sqrt{1-x^2}}-2 x=\frac{-x}{\sqrt{1-x^2}}$

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