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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} = \frac{- 1}{x} y + 2

\frac{d}{d t} (5 sin (t))

2 (sin (2 t)) e^{- 2 t}

\frac{d}{d x} (x ln (\frac{x}{4}))

\frac{2}{s ^{2}}

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