What is (\partial)/(\partial x)(1+xln(xy-7)) ?

The answer to (\partial)/(\partial x)(1+xln(xy-7)) is (xy)/(xy-7)+ln(xy-7)

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(\partial)/(\partial x)(1+xln(xy-7))

\frac{\partial}{\partial x} (1 + x ln (x y - 7))

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

Solution steps

\frac{\partial}{\partial x} (1 + 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} (1) + \frac{\partial}{\partial x} (x ln (x y - 7))

\frac{\partial}{\partial x} (1) = 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{\partial ^{2}}{\partial x \partial y} ((1 + 2 x y^{2})^{3})

n = 1 \sum \infty 4 (2.1)^{n - 1}

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

t \frac{d y}{d t} = t^{3} + 8 t^{3} y

\int 9 cos (θ) d θ

What is (\partial)/(\partial x)(1+xln(xy-7)) ?
The answer to (\partial)/(\partial x)(1+xln(xy-7)) is (xy)/(xy-7)+ln(xy-7)