What is (\partial)/(\partial y)(((e^{xy}))/(x+y)) ?

The answer to (\partial)/(\partial y)(((e^{xy}))/(x+y)) is (e^{xy}x(x+y)-e^{xy})/((x+y)^2)

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(\partial)/(\partial y)(((e^{xy}))/(x+y))

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial y} ( e ^{x y} ) ( x + y ) - \frac{\partial}{\partial y} ( x + y ) e ^{x y}}{( x + y ) ^{2}}

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

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

= \frac{e ^{x y} x ( x + y ) - 1 \cdot e ^{x y}}{( x + y ) ^{2}}

Simplify

= \frac{e ^{x y} x ( x + y ) - e ^{x y}}{( x + y ) ^{2}}

\frac{d}{d x} (\frac{8 - x + 3 x ^{2}}{2 - 9 x})

x \to 2 lim (\frac{x + 7}{x - 2})

\frac{d}{d x} (\frac{2 x}{3 - tan ( x )})

- 3 x

\frac{d}{d x} (5 y^{3} + (x - 2)^{2} - 4 - e^{x - 2 y})

What is (\partial)/(\partial y)(((e^{xy}))/(x+y)) ?
The answer to (\partial)/(\partial y)(((e^{xy}))/(x+y)) is (e^{xy}x(x+y)-e^{xy})/((x+y)^2)