What is (\partial)/(\partial y)(xy+1/x+1/y) ?

The answer to (\partial)/(\partial y)(xy+1/x+1/y) is x-1/(y^2)

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(\partial)/(\partial y)(xy+1/x+1/y)

\frac{\partial}{\partial y} (x y + \frac{1}{x} + \frac{1}{y})

x - \frac{1}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (x y + \frac{1}{x} + \frac{1}{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{1}{x}) + \frac{\partial}{\partial y} (\frac{1}{y})

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

\frac{\partial}{\partial y} (\frac{1}{x}) = 0

\frac{\partial}{\partial y} (\frac{1}{y}) = - \frac{1}{y ^{2}}

= x + 0 - \frac{1}{y ^{2}}

Simplify

= x - \frac{1}{y ^{2}}

\int tan^{3} (10 x) d x

\int \frac{5 x - 3}{x ^{2} - 2 x - 3} d x

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

\frac{d}{d x} (sin (cos (4 x)))

\frac{1}{5 x ^{\frac{4}{5}}}

What is (\partial)/(\partial y)(xy+1/x+1/y) ?
The answer to (\partial)/(\partial y)(xy+1/x+1/y) is x-1/(y^2)