What is (\partial)/(\partial x)(1+xln(xy-9)) ?

The answer to (\partial)/(\partial x)(1+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)

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(\partial)/(\partial x)(1+xln(xy-9))

\frac{\partial}{\partial x} (1 + x ln (x y - 9))

\frac{x y}{x y - 9} + ln (x y - 9)

Solution steps

\frac{\partial}{\partial x} (1 + x ln (x y - 9))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (x ln (x y - 9))

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (x ln (x y - 9)) = ln (y x - 9) + \frac{y x}{y x - 9}

= 0 + ln (y x - 9) + \frac{y x}{y x - 9}

Simplify

= \frac{x y}{x y - 9} + ln (x y - 9)

What is (\partial)/(\partial x)(1+xln(xy-9)) ?
The answer to (\partial)/(\partial x)(1+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)