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

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

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

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

y - \frac{4}{x ^{2}}

Solution steps

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

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

\frac{\partial}{\partial x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{\partial}{\partial x} (\frac{2}{y}) = 0

= y - \frac{4}{x ^{2}} + 0

Simplify

= y - \frac{4}{x ^{2}}

y = ln (2) (x + 3)

x, 16

y = - 8 e^{- 2 x} - 9 e^{2 x} - 5 e^{x}

9 sin (3 x)

\int 1 - 49 x^{2} d x

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