{d over {dx}}({x^2}{e^x}sin x) = | vedclass

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Question

(A) To find the derivative of the product of three functions,we use the product rule: $\frac{d}{dx}(uvw) = u'vw + uv'w + uvw'$.Let $u = x^2$,$v = e^x$

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) To find the derivative of the product of three functions,we use the product rule: $\frac{d}{dx}(uvw) = u'vw + uv'w + uvw'$.Let $u = x^2$,$v = e^x$,and $w = \sin x$.Then $u' = 2x$,$v' = e^x$,and $w' = \cos x$.Applying the rule:$\frac{d}{dx}(x^2 e^x \sin x) = (2x)(e^x \sin x) + (x^2)(e^x \sin x) + (x^2)(e^x \cos x)$.Factor out $x e^x$ from the expression:$= x e^x (2 \sin x + x \sin x + x \cos x)$.

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

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