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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
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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