What is (\partial)/(\partial x)(9+xln(xy-7)) ?

The answer to (\partial)/(\partial x)(9+xln(xy-7)) is (xy)/(xy-7)+ln(xy-7)

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(\partial)/(\partial x)(9+xln(xy-7))

\frac{\partial}{\partial x} (9 + x ln (x y - 7))

\frac{x y}{x y - 7} + ln (x y - 7)

Solution steps

\frac{\partial}{\partial x} (9 + x ln (x y - 7))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (9) + \frac{\partial}{\partial x} (x ln (x y - 7))

\frac{\partial}{\partial x} (9) = 0

\frac{\partial}{\partial x} (x ln (x y - 7)) = ln (y x - 7) + \frac{y x}{y x - 7}

= 0 + ln (y x - 7) + \frac{y x}{y x - 7}

Simplify

= \frac{x y}{x y - 7} + ln (x y - 7)

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What is (\partial)/(\partial x)(9+xln(xy-7)) ?
The answer to (\partial)/(\partial x)(9+xln(xy-7)) is (xy)/(xy-7)+ln(xy-7)