What is (\partial)/(\partial y)(6+xln(xy-5)) ?

The answer to (\partial)/(\partial y)(6+xln(xy-5)) is (x^2)/(xy-5)

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(\partial)/(\partial y)(6+xln(xy-5))

\frac{\partial}{\partial y} (6 + x ln (x y - 5))

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

Solution steps

\frac{\partial}{\partial y} (6 + 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} (6) + \frac{\partial}{\partial y} (x ln (x y - 5))

\frac{\partial}{\partial y} (6) = 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 3 sin^{3} (x) cos^{7} (x) d x

x = 16 - y^{2}, x = y^{2} - 16

n = 6 \sum \infty \frac{3 n}{12 n}

y^{^{'''}} + y^{^{'}} = 2 x^{2}

f (x) = e^{t a n (x)}

What is (\partial)/(\partial y)(6+xln(xy-5)) ?
The answer to (\partial)/(\partial y)(6+xln(xy-5)) is (x^2)/(xy-5)