What is (\partial)/(\partial y)(6+xln(xy-7)) ?

The answer to (\partial)/(\partial y)(6+xln(xy-7)) is (x^2)/(xy-7)

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(\partial)/(\partial y)(6+xln(xy-7))

\frac{\partial}{\partial y} (6 + x ln (x y - 7))

\frac{x ^{2}}{x y - 7}

Solution steps

\frac{\partial}{\partial y} (6 + x ln (x y - 7))

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (6) + \frac{\partial}{\partial y} (x ln (x y - 7))

\frac{\partial}{\partial y} (6) = 0

\frac{\partial}{\partial y} (x ln (x y - 7)) = \frac{x ^{2}}{x y - 7}

= 0 + \frac{x ^{2}}{x y - 7}

Simplify

= \frac{x ^{2}}{x y - 7}

\frac{\partial}{\partial x} (x y (1 - x - y))

\frac{d}{d x} (\frac{2}{sin ( x )})

sin (2 x), 0

\frac{d}{d x} (e^{- \frac{x}{6}})

y = x^{2} - 5

What is (\partial)/(\partial y)(6+xln(xy-7)) ?
The answer to (\partial)/(\partial y)(6+xln(xy-7)) is (x^2)/(xy-7)