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

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Question

(A) Let $y = e^{x\sin x}$.Applying the chain rule for differentiation,we have:$\frac{dy}{dx} = \frac{d}{dx}(e^{x\sin x}) = e^{x\sin x} \cdot \frac{d}{

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $y = e^{x\sin x}$.Applying the chain rule for differentiation,we have:$\frac{dy}{dx} = \frac{d}{dx}(e^{x\sin x}) = e^{x\sin x} \cdot \frac{d}{dx}(x\sin x)$.Using the product rule for $\frac{d}{dx}(x\sin x)$:$\frac{d}{dx}(x\sin x) = x \cdot \frac{d}{dx}(\sin x) + \sin x \cdot \frac{d}{dx}(x) = x\cos x + \sin x \cdot 1 = x\cos x + \sin x$.Therefore,$\frac{dy}{dx} = e^{x\sin x}(x\cos x + \sin x)$.Thus,the correct option is $A$.

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

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