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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = \log x.{e^{(\tan x + {x^2})}},$ then ${{dy} \over {dx}} = $
  • A
    ${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x + x)\log x} \right]$
  • B
    ${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x - x)\log x} \right]$
  • ✓
    ${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x + 2x)\log x} \right]$
  • D
    ${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x - 2x)\log x} \right]$
✓

Answer

Correct option: C.
${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x + 2x)\log x} \right]$
c
(c) $y = \log x.{e^{(\tan x + {x^{2)}}}}$

$\therefore \frac{{dy}}{{dx}} = {e^{(\tan x + {x^2})}}.\frac{1}{x} + \log x.{e^{(\tan x + {x^2})}}({\sec ^2}x + 2x)$

$ = {e^{(\tan x + {x^2})}}\left[ {\frac{1}{x} + ({{\sec }^2}x + 2x)\log x} \right]$.

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