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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

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

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

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

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

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

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

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

\int_{- 2}^{0} x + 2 d x

f (x) = 2 e^{2 x}

x \frac{d y}{d x} = y + x^{2} - y^{2}, x > 0

x = 2 + y + 3, x = 2 - y + 3, x = y - 1

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

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