What is (\partial)/(\partial x)(xe^xsin(y)) ?

The answer to (\partial)/(\partial x)(xe^xsin(y)) is sin(y)(e^x+e^xx)

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(\partial)/(\partial x)(xe^xsin(y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

\frac{\partial}{\partial x} (x) = 1

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

= sin (y) (1 \cdot e^{x} + e^{x} x)

Simplify

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

\int \frac{x ^{4}}{1 - x ^{2}} d x

(x^{3} - 12 x) (3 x^{2} + 2 x)

\frac{d}{d x} ((2^{x} \cdot x^{- 2})^{3 x - 1})

(3 x e^{x})^{^{'}}

\int x \frac{d}{1} (y) d x

What is (\partial)/(\partial x)(xe^xsin(y)) ?
The answer to (\partial)/(\partial x)(xe^xsin(y)) is sin(y)(e^x+e^xx)