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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

cos (x) \frac{π}{4}

x \to \infty lim (tan (x))

\frac{d}{d x} (\frac{3}{( x + 1 ) ^{2}})

y^{^{''}} = 13 (y^{^{'}})^{2}

\int \frac{13}{x ( x ^{2} + 25 )} d x

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