MCQ
If $y = {\cot ^{ - 1}}\left( {{{1 + x} \over {1 - x}}} \right)$, then ${{dy} \over {dx}} = $
- A${1 \over {1 + {x^2}}}$
- ✓$ - {1 \over {1 + {x^2}}}$
- C${2 \over {1 + {x^2}}}$
- D$ - {2 \over {1 + {x^2}}}$
$\frac{{dy}}{{dx}} = - \frac{1}{{1 + {{\left( {\frac{{1 + x}}{{1 - x}}} \right)}^2}}}\left[ {\frac{{(1 - x) + (1 + x)}}{{{{(1 - x)}^2}}}} \right]$
$ = - \frac{{2{{(1 - x)}^2}}}{{2(1 + {x^2})(1 - {x^2})}} = - \frac{1}{{1 + {x^2}}}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.