What is (\partial)/(\partial y)(1+xln(xy-5)) ?

The answer to (\partial)/(\partial y)(1+xln(xy-5)) is (x^2)/(xy-5)

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(\partial)/(\partial y)(1+xln(xy-5))

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

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

Solution steps

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

\frac{\partial}{\partial y} (1) = 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}

\frac{d}{d x} (7 sin (2 x))

\frac{d}{d x} ((2 x + 3)^{5})

y = 3 x^{2} - 2 x - 2 e n x = 1

\int_{0}^{π} sin (t) e^{- s t} d t

\frac{d}{d x} (sec (x) - 5 x^{4})

What is (\partial)/(\partial y)(1+xln(xy-5)) ?
The answer to (\partial)/(\partial y)(1+xln(xy-5)) is (x^2)/(xy-5)