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

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

Popular >

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

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

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

Solution steps

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

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

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

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

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

Simplify

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

(- 34, 74), (- 33, 44)

\frac{\partial}{\partial u} (5 u^{2} v^{3} + 2 u^{2} + 7 v)

\frac{d y}{d x} = \frac{y}{2 ( x + y )}

ln (cos^{2} (x) + sin^{2} (x))

\int (x^{2})^{\frac{1}{2}} d x

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