What is (\partial)/(\partial x)(e^xsin(x)) ?

The answer to (\partial)/(\partial x)(e^xsin(x)) is e^xsin(x)+cos(x)e^x

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(\partial)/(\partial x)(e^xsin(x))

\frac{\partial}{\partial x} (e^{x} sin (x))

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

Solution steps

\frac{\partial}{\partial x} (e^{x} sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = sin (x)

= \frac{\partial}{\partial x} (e^{x}) sin (x) + \frac{\partial}{\partial x} (sin (x)) e^{x}

\frac{\partial}{\partial x} (e^{x}) = e^{x}

\frac{\partial}{\partial x} (sin (x)) = cos (x)

= e^{x} sin (x) + cos (x) e^{x}

n \to \infty lim (\frac{n ^{2} + 3}{n ^{3} n + n ^{\frac{5}{2}}})

\int \frac{x ^{3} + 3 x - 2}{x ^{2} - x} d x

\frac{d}{d x} (\frac{7}{x ^{7}})

\int_{1}^{8} x^{- \frac{8}{3}} d x

y = x^{2} + 9, y = 10 + 2 x

What is (\partial)/(\partial x)(e^xsin(x)) ?
The answer to (\partial)/(\partial x)(e^xsin(x)) is e^xsin(x)+cos(x)e^x