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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{( z - 2 y ) ^{2}} \frac{\partial}{\partial z} (z - 2 y)

= - \frac{1}{( z - 2 y ) ^{2}} \frac{\partial}{\partial z} (z - 2 y)

\frac{\partial}{\partial z} (z - 2 y) = 1

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

Simplify

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

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

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

\int sin (\frac{1}{7}) x d x

h \to 0 lim \frac{( ( h - 5 ) ^{2} - 25 )}{( h )}

\frac{d}{d y} (2 x y^{3})

\int - \frac{1}{s} e^{- s t} d t

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