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

The answer to (\partial)/(\partial x)(e^xxy) is y(e^xx+e^x)

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

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

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

Simplify

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

\frac{d y}{d x} = \frac{x y + 7 x - y - 7}{x y - 2 x + 8 y - 16}

\frac{\partial}{\partial x} (3 x^{2} y^{2} + 3)

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

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

\frac{( e ^{x} - e ^{- x} )}{2}

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