What is (\partial)/(\partial x)(8+xln(xy-7)) ?

The answer to (\partial)/(\partial x)(8+xln(xy-7)) is (xy)/(xy-7)+ln(xy-7)

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(\partial)/(\partial x)(8+xln(xy-7))

\frac{\partial}{\partial x} (8 + x ln (x y - 7))

\frac{x y}{x y - 7} + ln (x y - 7)

Solution steps

\frac{\partial}{\partial x} (8 + x ln (x y - 7))

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 - 7))

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

\frac{\partial}{\partial x} (x ln (x y - 7)) = ln (y x - 7) + \frac{y x}{y x - 7}

= 0 + ln (y x - 7) + \frac{y x}{y x - 7}

Simplify

= \frac{x y}{x y - 7} + ln (x y - 7)

\frac{d}{d x} (3^{\frac{x}{2}})

\frac{d}{d x} (x^{3} + x^{2} - 5 x)

\int x \cdot e^{5 x} d x

\int (\frac{1}{x ^{2}} - 1) d x

x \to 0 lim (\frac{5 sin ( x )}{x})

What is (\partial)/(\partial x)(8+xln(xy-7)) ?
The answer to (\partial)/(\partial x)(8+xln(xy-7)) is (xy)/(xy-7)+ln(xy-7)