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

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

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

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

\frac{y}{z ^{2}}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial z} (\frac{x}{y}) = 0

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

= 0 - (- \frac{y}{z ^{2}})

Simplify

= \frac{y}{z ^{2}}

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

x \to 0 lim (x^{- \frac{5}{l n ( x )}})

\frac{\partial}{\partial x} (x^{2} + 3 y^{2})

f (x) = x^{2} + 8, (5, 33)

y = \frac{8}{x}, (2, 4)

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