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)

(\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}}

x, 16

f (x) = e^{10 x}

\frac{\partial}{\partial y} (x^{2} y^{2} e^{2 x y})

(x^{\frac{3}{2}})^{^{'}}

\frac{\partial}{\partial y} (ln (x^{2} + y^{2}))

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)