d dx e^ x x = - Vidyadip

MCQ

${d \over {dx}}{e^{x\sin x}} = $

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

✓

Answer

Correct option: A.

${e^{x\sin x}}(x\cos x + \sin x)$

a
(a) Let $y = {e^{x\sin x}}$==> $\log y = x\sin x$

$\therefore \frac{1}{y}\frac{{dy}}{{dx}} = \sin x + x\cos x$ or

$\frac{{dy}}{{dx}} = {e^{x\sin x}}(\sin x + x\cos x)$.

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