What is (\partial)/(\partial x)(3+xln(xy-9)) ?

The answer to (\partial)/(\partial x)(3+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)

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(\partial)/(\partial x)(3+xln(xy-9))

\frac{\partial}{\partial x} (3 + x ln (x y - 9))

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

Solution steps

\frac{\partial}{\partial x} (3 + 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} (3) + \frac{\partial}{\partial x} (x ln (x y - 9))

\frac{\partial}{\partial x} (3) = 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)

y^{^{''}} + 3 y^{^{'}} + 3.25 y = 3 cos (t) - 1.5 sin (t)

y^{^{'}} = \frac{e ^{x + y}}{1 + e ^{x}}

y = \frac{29}{x ^{3}}, [1, 10]

x \to 4 lim (4 - 2)

\int (x^{3} + x)^{2} d x

What is (\partial)/(\partial x)(3+xln(xy-9)) ?
The answer to (\partial)/(\partial x)(3+xln(xy-9)) is (xy)/(xy-9)+ln(xy-9)