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

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

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

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

\frac{5 x}{y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

5 x \frac{1}{x y} x : \frac{5 x}{y}

= \frac{5 x}{y}

\frac{\partial}{\partial x} (y^{2} cos (x))

\frac{\partial}{\partial x} (sin (9 x + yz))

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

\int x (5 x - 3)^{2} d x

\int e^{3 x} + \frac{1}{x} d x

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