What is (\partial)/(\partial x)(2+xln(xy-9)) ?

The answer to (\partial)/(\partial x)(2+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)

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(\partial)/(\partial x)(2+xln(xy-9))

\frac{\partial}{\partial x} (2 + x ln (x y - 9))

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

Solution steps

\frac{\partial}{\partial x} (2 + 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} (2) + \frac{\partial}{\partial x} (x ln (x y - 9))

\frac{\partial}{\partial x} (2) = 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)

u^{1}

f (x) = \frac{3}{8} x^{4} - 2 - \frac{10}{x}

f (x) = (3 x^{2} - 1)^{2}

2 x, y = \frac{1}{3} x

\frac{d}{d x} (x^{3} + 3 x^{2} - 9 x + 4)

What is (\partial)/(\partial x)(2+xln(xy-9)) ?
The answer to (\partial)/(\partial x)(2+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)