What is (\partial)/(\partial x)((e^{xy})/(x+1)) ?

The answer to (\partial)/(\partial x)((e^{xy})/(x+1)) is (e^{xy}y(x+1)-e^{xy})/((x+1)^2)

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(\partial)/(\partial x)((e^{xy})/(x+1))

\frac{\partial}{\partial x} (\frac{e ^{x y}}{x + 1})

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

Solution steps

\frac{\partial}{\partial x} (\frac{e ^{x y}}{x + 1})

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

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

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

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

Simplify

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

What is (\partial)/(\partial x)((e^{xy})/(x+1)) ?
The answer to (\partial)/(\partial x)((e^{xy})/(x+1)) is (e^{xy}y(x+1)-e^{xy})/((x+1)^2)