What is (\partial)/(\partial x)((2xy)/(x+y)) ?

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

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(\partial)/(\partial x)((2xy)/(x+y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 2 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}}

= 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

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

Simplify

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

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

\int w w^{2} - ln (3) d w

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

\int \frac{3 x ^{2} - 2 x + 5}{x ^{2}} d x

x^{3} \frac{d y}{d x} + y^{2} = x^{2} y

\frac{3 x ^{2} + 1}{2 x ^{2} - 5}

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