What is (\partial)/(\partial x)(8+xln(xy-9)) ?

The answer to (\partial)/(\partial x)(8+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)

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(\partial)/(\partial x)(8+xln(xy-9))

\frac{\partial}{\partial x} (8 + x ln (x y - 9))

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

Solution steps

\frac{\partial}{\partial x} (8 + 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} (8) + \frac{\partial}{\partial x} (x ln (x y - 9))

\frac{\partial}{\partial x} (8) = 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)

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

\int_{- 2}^{0} (x - 2) (x + 1) d x

y = 8 x, y = \frac{5}{2} x, y = 9 - x^{2}

x \to 4 - lim (4 - x)

\frac{d y}{d x} = \frac{4}{x e ^{y}}

What is (\partial)/(\partial x)(8+xln(xy-9)) ?
The answer to (\partial)/(\partial x)(8+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)