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

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

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

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

ln (x)

Solution steps

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

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

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

= 0 + ln (x)

Simplify

= ln (x)

\int \frac{1}{b - a y} d y

\int (x^{2} - 4 x + 5) d x

4 + 3 x

\frac{d}{d x} (arcsin (\frac{x}{10}))

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

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