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

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

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

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

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

Solution steps

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

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{y}{x})

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

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

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

f (x) = x - 8, at x = 9

\int 0.06 e^{0.04 x} d x

\int 3 x^{2} cos (x) d x

n = 0 \sum \infty \frac{n !}{10 7 ^{n}}

\frac{d}{d x} (\frac{x ^{2}}{5 x + 2})

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