What is (\partial)/(\partial x)(9+ln(xy-5)) ?

The answer to (\partial)/(\partial x)(9+ln(xy-5)) is y/(xy-5)

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(\partial)/(\partial x)(9+ln(xy-5))

\frac{\partial}{\partial x} (9 + ln (x y - 5))

\frac{y}{x y - 5}

Solution steps

\frac{\partial}{\partial x} (9 + ln (x y - 5))

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} (ln (x y - 5))

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

\frac{\partial}{\partial x} (ln (x y - 5)) = \frac{y}{y x - 5}

= 0 + \frac{y}{y x - 5}

Simplify

= \frac{y}{x y - 5}

\int \frac{8 x ^{2} + 3 x - 6}{( x ^{2} - 4 ) ( x + 2 )} d x

\frac{2}{x} - 3 e^{x} + 3 e^{4}

75 (1 - \frac{5}{x})

n = 1 \sum \infty (\frac{2}{5})^{n - 1}

x \to 0 lim (\frac{5 - 5 cos ( x )}{x})

What is (\partial)/(\partial x)(9+ln(xy-5)) ?
The answer to (\partial)/(\partial x)(9+ln(xy-5)) is y/(xy-5)