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{\partial}{\partial z} (x^{2} y + y z^{3} + z^{5} x)

y \to 0 lim (\frac{y ^{2}}{y ^{2}})

\int x^{3} 25 + x^{2} d x

\int \frac{5 x ^{2}}{x ^{2} + x - 6} d x

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

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