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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{x y - 5} \frac{\partial}{\partial y} (x y - 5)

= \frac{1}{x y - 5} \frac{\partial}{\partial y} (x y - 5)

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

= x \frac{1}{x y - 5} x

Simplify

x \frac{1}{x y - 5} x : \frac{x ^{2}}{x y - 5}

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

\int_{0}^{9} (\frac{1}{3} x - 2) d x

(5 + x) y^{^{'}} - y = 0

\int u - 1 d u

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

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

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