What is (\partial)/(\partial y)(m/y-625 y/x) ?

The answer to (\partial)/(\partial y)(m/y-625 y/x) is -m/(y^2)-(625)/x

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(\partial)/(\partial y)(m/y-625 y/x)

\frac{\partial}{\partial y} (\frac{m}{y} - 625 \frac{y}{x})

- \frac{m}{y ^{2}} - \frac{625}{x}

Solution steps

\frac{\partial}{\partial y} (\frac{m}{y} - 625 \cdot \frac{y}{x})

Simplify

\frac{m}{y} - 625 \cdot \frac{y}{x} : \frac{m}{y} - \frac{625 y}{x}

= \frac{\partial}{\partial y} (\frac{m}{y} - \frac{625 y}{x})

Treat

m, x

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (\frac{m}{y}) - \frac{\partial}{\partial y} (\frac{625 y}{x})

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

\frac{\partial}{\partial y} (\frac{625 y}{x}) = \frac{625}{x}

= - \frac{m}{y ^{2}} - \frac{625}{x}

What is (\partial)/(\partial y)(m/y-625 y/x) ?
The answer to (\partial)/(\partial y)(m/y-625 y/x) is -m/(y^2)-(625)/x