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

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

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

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

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

Solution steps

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

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} (yz)

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

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

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

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