What is (\partial)/(\partial x)(8+xln(xy-5)) ?

The answer to (\partial)/(\partial x)(8+xln(xy-5)) is (xy)/(xy-5)+ln(xy-5)

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(\partial)/(\partial x)(8+xln(xy-5))

\frac{\partial}{\partial x} (8 + x ln (x y - 5))

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

Solution steps

\frac{\partial}{\partial x} (8 + x ln (x y - 5))

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 - 5))

\frac{\partial}{\partial x} (8) = 0

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

= 0 + ln (y x - 5) + \frac{y x}{y x - 5}

Simplify

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

\int \frac{x ^{2}}{u} d u

f (x) = x^{2} arctan (4 x)

\frac{\partial}{\partial y} (e^{x} + y^{2})

h (x) = \frac{7}{x ^{2}}

\frac{( s + 1 )}{( s \cdot ( s ^{2} + s + 1 ) )}

What is (\partial)/(\partial x)(8+xln(xy-5)) ?
The answer to (\partial)/(\partial x)(8+xln(xy-5)) is (xy)/(xy-5)+ln(xy-5)