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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x y - 9)

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot ln (x y - 9) + \frac{y}{y x - 9} x

Simplify

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

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

\frac{4 x ^{2} + 2 x + 8}{x}

x \to \frac{1}{2} lim (10 x^{2} - 9 x + 2)

\int_{1}^{\infty} \frac{1}{x} d x

(0, 2), (- 5, - 1)

n = 1 \sum \infty \frac{1}{2 ^{n + 1}}

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