What is (\partial)/(\partial y)(5+xln(xy-7)) ?

The answer to (\partial)/(\partial y)(5+xln(xy-7)) is (x^2)/(xy-7)

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(\partial)/(\partial y)(5+xln(xy-7))

\frac{\partial}{\partial y} (5 + x ln (x y - 7))

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

Solution steps

\frac{\partial}{\partial y} (5 + 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} (5) + \frac{\partial}{\partial y} (x ln (x y - 7))

\frac{\partial}{\partial y} (5) = 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}

x^{2} + \frac{1}{x ^{2}}

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

\frac{x ^{2}}{100} + 8 + \frac{20}{x}

\int \frac{1.05}{1 + 100 e ^{- 0.285 x}} d x

n = 0 \sum \infty \frac{4}{5 ^{n}}

What is (\partial)/(\partial y)(5+xln(xy-7)) ?
The answer to (\partial)/(\partial y)(5+xln(xy-7)) is (x^2)/(xy-7)