What is (\partial)/(\partial x)((x-y)/(x+y)-y^3) ?

The answer to (\partial)/(\partial x)((x-y)/(x+y)-y^3) is (2y)/((x+y)^2)

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(\partial)/(\partial x)((x-y)/(x+y)-y^3)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{3}) = 0

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

Simplify

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

\frac{3}{( s + 1 ) ^{2} + 9}

\frac{d}{d x} (tan (13 x))

2 e^{4 x} cos (5 x)

\frac{\partial}{\partial x} (ln (x^{7} - y^{3}))

What is (\partial)/(\partial x)((x-y)/(x+y)-y^3) ?
The answer to (\partial)/(\partial x)((x-y)/(x+y)-y^3) is (2y)/((x+y)^2)