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

MCQ

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

✓
${e^x}(\log \sin 2x + 2\cot 2x)$
B
${e^x}(\log \cos 2x + 2\cot 2x)$
C
${e^x}(\log \cos 2x + \cot 2x)$
D
None of these

✓

Answer

Correct option: A.

${e^x}(\log \sin 2x + 2\cot 2x)$

a
(a) $\frac{d}{{dx}}({e^x}\log \sin 2x) = {e^x}\log \sin 2x + 2{e^x}\frac{1}{{\sin 2x}}\cos 2x$

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

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