d dx e^ - a x^2 ( x) = - Vidyadip

MCQ

${d \over {dx}}\{ {e^{ - a{x^2}}}\log (\sin x)\} = $

A
${e^{ - a{x^2}}}(\cot x + 2ax\log \sin x)$
B
${e^{ - a{x^2}}}(\cot x + ax\log \sin x)$
✓
${e^{ - a{x^2}}}(\cot x - 2ax\log \sin x)$
D
None of these

✓

Answer

Correct option: C.

${e^{ - a{x^2}}}(\cot x - 2ax\log \sin x)$

c
(c) $\frac{d}{{dx}}\{ {e^{ - a{x^2}}}\log (\sin x)\} $

$ = {e^{ - a{x^2}}}( - 2ax).\log (\sin x) + {e^{ - a{x^2}}}\cot x$

$ = {e^{ - ax}}^2[\cot x - 2ax\log (\sin x)]$.

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