What is (\partial)/(\partial y)(xy+8/x+8/y) ?

The answer to (\partial)/(\partial y)(xy+8/x+8/y) is x-8/(y^2)

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(\partial)/(\partial y)(xy+8/x+8/y)

\frac{\partial}{\partial y} (x y + \frac{8}{x} + \frac{8}{y})

x - \frac{8}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (x y + \frac{8}{x} + \frac{8}{y})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x y) + \frac{\partial}{\partial y} (\frac{8}{x}) + \frac{\partial}{\partial y} (\frac{8}{y})

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

\frac{\partial}{\partial y} (\frac{8}{x}) = 0

\frac{\partial}{\partial y} (\frac{8}{y}) = - \frac{8}{y ^{2}}

= x + 0 - \frac{8}{y ^{2}}

Simplify

= x - \frac{8}{y ^{2}}

\frac{d}{d x} (7 - 2 x)

x \to 0 lim (x cot (\frac{7}{11} x))

\int_{1}^{e} x^{2} ln (x) d x

\frac{d y}{d x} = (x y^{2})

x \to 0 lim (\frac{3 x}{tan ( x )})

What is (\partial)/(\partial y)(xy+8/x+8/y) ?
The answer to (\partial)/(\partial y)(xy+8/x+8/y) is x-8/(y^2)