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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= y \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

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

Simplify

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

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

\frac{d}{d x} (- \frac{1}{1 + x ^{2}})

\frac{d}{d y} (4 y^{2})

ln (x + x^{2} - 1)

\frac{d}{d x} (6 x + 6 x^{2})

\frac{d v}{d t} = 0.025 \cdot 7 - \frac{v}{2000}, v (0) = 100

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