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

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(A) Let $y = x^2 e^x \sin x$. Applying the product rule for three functions,$\frac{d}{dx}(uvw) = u'vw + uv'w + uvw'$.Here,$u = x^2$,$v = e^x$,and $w =

Vedclass · Accepted Answer

$x e^x (2 \sin x + x \sin x + x \cos x)$

Vedclass · Answer

(A) Let $y = x^2 e^x \sin x$. Applying the product rule for three functions,$\frac{d}{dx}(uvw) = u'vw + uv'w + uvw'$.Here,$u = x^2$,$v = e^x$,and $w = \sin x$.$\frac{dy}{dx} = \frac{d}{dx}(x^2) \cdot e^x \sin x + x^2 \cdot \frac{d}{dx}(e^x) \cdot \sin x + x^2 \cdot e^x \cdot \frac{d}{dx}(\sin x)$$= 2x e^x \sin x + x^2 e^x \sin x + x^2 e^x \cos x$$= x e^x (2 \sin x + x \sin x + x \cos x)$.

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

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