What is (\partial)/(\partial y)(3+xln(xy-7)) ?

The answer to (\partial)/(\partial y)(3+xln(xy-7)) is (x^2)/(xy-7)

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(\partial)/(\partial y)(3+xln(xy-7))

\frac{\partial}{\partial y} (3 + x ln (x y - 7))

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

Solution steps

\frac{\partial}{\partial y} (3 + 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} (3) + \frac{\partial}{\partial y} (x ln (x y - 7))

\frac{\partial}{\partial y} (3) = 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}

f (x) = 1 + x^{2}

\frac{\partial}{\partial x} (5 arctan (x))

x \to + (- 2) lim (lo g_{2} (8))

\int e^{- x + 1} d x

\int_{- 1}^{2} x - 2 ∣ x ∣ d x

What is (\partial)/(\partial y)(3+xln(xy-7)) ?
The answer to (\partial)/(\partial y)(3+xln(xy-7)) is (x^2)/(xy-7)