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

The answer to (\partial)/(\partial y)(x/y-y/z) is -x/(y^2)-1/z

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

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

- \frac{x}{y ^{2}} - \frac{1}{z}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= - \frac{x}{y ^{2}} - \frac{1}{z}

\frac{d}{d x} (e^{- 2 x} sin (3 x))

x \to - 1 lim (2 x^{2} - 5 x + 1)

x^{\frac{7}{3}}

\frac{d}{d x} (- x + 6)

- \frac{1}{2} y = \frac{d y}{d t}

What is (\partial)/(\partial y)(x/y-y/z) ?
The answer to (\partial)/(\partial y)(x/y-y/z) is -x/(y^2)-1/z