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

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

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(\partial)/(\partial y)((x+y)/(z-2y))

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

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

Solution steps

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

Treat

x, z

as constants

Apply the Quotient Rule:

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

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

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

\frac{\partial}{\partial y} (z - 2 y) = - 2

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

Simplify

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

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

x \to 0 lim ((1 + 2 (\frac{1}{y}))^{\frac{1}{x}})

\int_{2}^{3} \frac{19}{3 - x} d x

y^{^{'}} = 5 x e^{y}

\frac{d}{d x} (x ln (x y))

\int x^{3} 36 - x^{2} d x

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