What is (\partial)/(\partial x)(xy+2/x+4/y) ?

The answer to (\partial)/(\partial x)(xy+2/x+4/y) is y-2/(x^2)

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(\partial)/(\partial x)(xy+2/x+4/y)

\frac{\partial}{\partial x} (x y + \frac{2}{x} + \frac{4}{y})

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

Solution steps

\frac{\partial}{\partial x} (x y + \frac{2}{x} + \frac{4}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (\frac{2}{x}) + \frac{\partial}{\partial x} (\frac{4}{y})

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

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

\frac{\partial}{\partial x} (\frac{4}{y}) = 0

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

Simplify

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

What is (\partial)/(\partial x)(xy+2/x+4/y) ?
The answer to (\partial)/(\partial x)(xy+2/x+4/y) is y-2/(x^2)