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5. continuity and differentiation — ગણિત ધોરણ 12 સાયન્સ — Question

Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિત5. continuity and differentiation1 Mark
MCQ
${d \over {dx}}{\tan ^{ - 1}}(\sec x + \tan x) = $
  • A
    $1$
  • ✓
    $1/2$
  • C
    $\cos x$
  • D
    $\sec x$
✓

Answer

Correct option: B.
$1/2$
b
(b) $\frac{d}{{dx}}{\tan ^{ - 1}}(\sec x + \tan x) = \frac{d}{{dx}}{\tan ^{ - 1}}\left( {\frac{{1 + \sin x}}{{\cos x}}} \right)$

$ = \frac{d}{{dx}}{\tan ^{ - 1}}\left( {\frac{{\sin \left( {\frac{x}{2}} \right) + \cos \left( {\frac{x}{2}} \right)}}{{\cos \left( {\frac{x}{2}} \right) - \sin \left( {\frac{x}{2}} \right)}}} \right) = \frac{d}{{dx}}\left( {\frac{\pi }{4} + \frac{x}{2}} \right) = \frac{1}{2}$.

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