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}

f (x) = x^{3} (x^{2} + 4)^{- 2}

4 \cdot e^{2 x}

\frac{d}{d x} (1 - \frac{3}{y} + x)

\int_{0}^{1} 2 x - 2 x d x

\int \frac{x ^{3} - 1}{x ^{4} - 4 x + 1} d 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