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

MCQ

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

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

✓

Answer

Correct option: A.

$x\,{e^x}(2\sin x + x\sin x + x\cos x)$

a
(a) $\frac{d}{{dx}}\left( {{x^2}{e^x}\sin x} \right) = {x^2}\frac{d}{{dx}}\left( {{e^x}\sin x} \right)$$ + {e^x}\sin x\frac{d}{{dx}}({x^2})$

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

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