What is (\partial)/(\partial y)(2+xln(xy-5)) ?

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

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(\partial)/(\partial y)(2+xln(xy-5))

\frac{\partial}{\partial y} (2 + x ln (x y - 5))

\frac{x ^{2}}{x y - 5}

Solution steps

\frac{\partial}{\partial y} (2 + x ln (x y - 5))

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (2) + \frac{\partial}{\partial y} (x ln (x y - 5))

\frac{\partial}{\partial y} (2) = 0

\frac{\partial}{\partial y} (x ln (x y - 5)) = \frac{x ^{2}}{x y - 5}

= 0 + \frac{x ^{2}}{x y - 5}

Simplify

= \frac{x ^{2}}{x y - 5}

\int \frac{1}{x ^{2} - 8 x - 12} d x

y^{^{''}} + 2 y^{^{'}} + y = x^{- 6} e^{- x}

\int \frac{x + 2}{x ^{2} + 3 x - 4} d x

\frac{\partial}{\partial x} (\frac{4}{36 - x ^{2}})

(2) (- 3.1)

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