What is (\partial}{\partial x}(y/z+z/x-\frac{xz)/y) ?

The answer to (\partial}{\partial x}(y/z+z/x-\frac{xz)/y) is -z/y-z/(x^2)

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(\partial}{\partial x}(y/z+z/x-\frac{xz)/y)

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 - \frac{z}{x ^{2}} - \frac{z}{y}

Simplify

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

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ln (1 - x)

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

What is (\partial}{\partial x}(y/z+z/x-\frac{xz)/y) ?
The answer to (\partial}{\partial x}(y/z+z/x-\frac{xz)/y) is -z/y-z/(x^2)