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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(e^x\right)\sin\left(x\right)+e^x\frac{d}{dx}\left(\sin\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx(e^xsin(x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. Applying the derivative of the exponential function. Simplify the derivative.