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

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

\int \frac{( x - 1 )}{x ^{3} + x ^{2} + 6 x} d x

x \to 4 - lim (4 x)

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

\int x^{2} e^{4 x^{3}} d x

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