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

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

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

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

y + \frac{1}{y}

Solution steps

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

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

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

= y + \frac{1}{y}

f (z) = e^{\frac{z}{z - 1}}

\frac{d}{d x} (5 (x^{3} - 4 x)^{- 3})

\int_{0}^{3} \frac{8 t}{( t - 4 ) ^{2}} d t

\int_{0}^{\frac{π}{2}} sin^{3} (2 x) d x

\frac{d}{d x} (e^{0.4 x} \cdot cos (0.2 x))

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