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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
${d \over {dx}}\left\{ {{e^x}\log (1 + {x^2})} \right\} = $
  • ✓
    ${e^x}\left[ {\log (1 + {x^2}) + {{2x} \over {1 + {x^2}}}} \right]$
  • B
    ${e^x}\left[ {\log (1 + {x^2}) - {{2x} \over {1 + {x^2}}}} \right]$
  • C
    ${e^x}\left[ {\log (1 + {x^2}) + {x \over {1 + {x^2}}}} \right]$
  • D
    ${e^x}\left[ {\log (1 + {x^2}) - {x \over {1 + {x^2}}}} \right]$
✓

Answer

Correct option: A.
${e^x}\left[ {\log (1 + {x^2}) + {{2x} \over {1 + {x^2}}}} \right]$
a
(a) $\frac{d}{{dx}}\{ {e^x}\log (1 + {x^2})\} = {e^x}\log (1 + {x^2}) + {e^x}\frac{1}{{(1 + {x^2})}}2x$

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

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