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Find dy dx of y = Sin−1 (x 2 − 2x + 1)

Posted by Devendra Kumar 2 years, 4 months ago

CBSE > Class 12 > Mathematics

1 answers

Preeti Dabral 2 years, 4 months ago

Given: $y = {\sin ^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right)$

To simplify the given Inverse Trigonometric function,we put, $x = \tan \theta$

$\Rightarrow y = {\sin ^{ - 1}}\left( {\frac{{2\tan \theta }}{{1 + {{\tan }^2}\theta }}} \right) = {\sin ^{ - 1}}\left( {\sin 2\theta } \right) = 2\theta$

$\Rightarrow y = 2{\tan ^{ - 1}}x$

$\Rightarrow \frac{{dy}}{{dx}} = 2.\frac{1}{{1 + {x^2}}} = \frac{2}{{1 + {x^2}}}$

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