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

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

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

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

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

Solution steps

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

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

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

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

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

Simplify

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

f (x) = (14 x - x^{2})^{3}

\int cos^{2} (x) sec^{2} (x) d x

n = 0 \sum \infty \frac{1}{5 n}

\int \frac{1 - x}{1 + x} \cdot \frac{1}{x ^{2}} d x

\int_{t}^{0} \frac{1}{1 + x ^{2}} d x

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