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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\int (2 π cos (π x)) d x

\int - sin (x) cos (x) d x

\int \frac{e ^{3}}{x} d x

x \to 0 lim (\frac{∣ x ∣}{4 x})

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