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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{2 x}{x + 5})

100 x

\int \frac{( 4 x + 3 )}{x ^{2} + 1} d x

x \to \infty lim (5 + \frac{4}{x})

y = (5 t - 1) (2 t - 3)^{- 1}

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