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

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

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

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

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

Solution steps

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

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

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

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

1 \cdot (x + y) - 1 \cdot x = y

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

\int \frac{x}{4 x - x ^{2}} d x

\int 2 x (x^{2} + 1)^{8} d x

(g (x))^{3}

x \to 0 lim (x^{3} e^{- x^{2}})

\int_{\frac{1}{2}}^{5} \frac{1}{( 2 x - 1 ) ^{\frac{1}{3}}} d x

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