What is (\partial)/(\partial y)(xln(y)-yln(x)) ?

The answer to (\partial)/(\partial y)(xln(y)-yln(x)) is x/y-ln(x)

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(\partial)/(\partial y)(xln(y)-yln(x))

\frac{\partial}{\partial y} (x ln (y) - y ln (x))

\frac{x}{y} - ln (x)

Solution steps

\frac{\partial}{\partial y} (x ln (y) - y ln (x))

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{x}{y} - ln (x)

\int \frac{x ^{4} - x ^{3} + 2 x ^{2} - 2 x - 8}{x ^{2} + 4} d x

x \to 4 lim (\frac{x}{x ^{2} - 3 x})

y^{^{'}} = (x + 1) y^{2}

\int \frac{x ^{3}}{x ^{2} + 5} d x

\frac{d}{d x} (\frac{d y}{d x}) = 4 x

What is (\partial)/(\partial y)(xln(y)-yln(x)) ?
The answer to (\partial)/(\partial y)(xln(y)-yln(x)) is x/y-ln(x)