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

The answer to (\partial)/(\partial x)(-xln(x)+xln(y)+y) is ln(y)-ln(x)-1

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

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

ln (y) - ln (x) - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x ln (x)) = ln (x) + 1

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

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

= - (ln (x) + 1) + ln (y) + 0

Simplify

= ln (y) - ln (x) - 1

What is (\partial)/(\partial x)(-xln(x)+xln(y)+y) ?
The answer to (\partial)/(\partial x)(-xln(x)+xln(y)+y) is ln(y)-ln(x)-1