What is (\partial)/(\partial x)((xy)/(x+y)+z) ?

The answer to (\partial)/(\partial x)((xy)/(x+y)+z) is (y^2)/((x+y)^2)

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(\partial)/(\partial x)((xy)/(x+y)+z)

\frac{\partial}{\partial x} (\frac{x y}{x + y} + z)

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

Solution steps

\frac{\partial}{\partial x} (\frac{x y}{x + y} + z)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (z) = 0

= \frac{y ^{2}}{( x + y ) ^{2}} + 0

Simplify

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

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What is (\partial)/(\partial x)((xy)/(x+y)+z) ?
The answer to (\partial)/(\partial x)((xy)/(x+y)+z) is (y^2)/((x+y)^2)