What is (\partial)/(\partial x)(xln(xy-5)) ?

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

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(\partial)/(\partial x)(xln(xy-5))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = ln (x y - 5)

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

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

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

= 1 \cdot ln (x y - 5) + \frac{y}{y x - 5} x

Simplify

1 \cdot ln (x y - 5) + \frac{y}{y x - 5} x : ln (x y - 5) + \frac{x y}{x y - 5}

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

x \to 3 lim (x^{2} + 4)

\int_{- 1}^{1} x (1.5 x^{2}) d x

\frac{d}{d x} (ln (\frac{x + 1}{x - 1}))

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

2 cos (2 t)

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