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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If $y = (1 + {x^2}){\tan ^{ - 1}}x - x,$ then ${{dy} \over {dx}} = $
  • A
    ${\tan ^{ - 1}}x$
  • ✓
    $2x{\tan ^{ - 1}}x$
  • C
    $2x{\tan ^{ - 1}}x - 1$
  • D
    ${{2x} \over {{{\tan }^{ - 1}}x}}$
✓

Answer

Correct option: B.
$2x{\tan ^{ - 1}}x$
b
(b) $y = (1 + {x^2}){\tan ^{ - 1}}x - x$

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

$= 2x{\tan ^{ - 1}}x.$

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