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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

n \to \infty lim (\frac{n}{5})

x \to 5 lim (12)

\frac{d}{d x} (x^{4} + \frac{2}{x})

\frac{d}{d x} (3 x^{2} + 2 x + 4)

\int_{0}^{2} \frac{1}{x ^{\frac{1}{3}}} d x

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