If y = ^ - 1 ( x^2 ), then dy dx is equal to - Vidyadip

MCQ

If $y = {\cot ^{ - 1}}({x^2})$, then ${{dy} \over {dx}}$ is equal to

A
${{2x} \over {1 + {x^4}}}$
B
${{2x} \over {\sqrt {1 + 4x} }}$
✓
${{ - 2x} \over {1 + {x^4}}}$
D
${{ - 2x} \over {\sqrt {1 + {x^2}} }}$

✓

Answer

Correct option: C.

${{ - 2x} \over {1 + {x^4}}}$

c
(c) $y = {\cot ^{ - 1}}\left( {{x^2}} \right)$

$\frac{{dy}}{{dx}} = \frac{{ - 1}}{{1 + {{({x^2})}^2}}}\frac{d}{{dx}}({x^2}) $

$= \frac{{ - 1}}{{1 + {x^4}}}(2x) = \frac{{ - 2x}}{{1 + {x^4}}}$.

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