What is (\partial)/(\partial y)(4xln(xy)) ?

The answer to (\partial)/(\partial y)(4xln(xy)) is (4x)/y

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(\partial)/(\partial y)(4xln(xy))

\frac{\partial}{\partial y} (4 x ln (x y))

\frac{4 x}{y}

Solution steps

\frac{\partial}{\partial y} (4 x ln (x y))

Treat

x

as a constant

Take the constant out:

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

= 4 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

= 4 x \frac{1}{x y} x

Simplify

4 x \frac{1}{x y} x : \frac{4 x}{y}

= \frac{4 x}{y}

\frac{d y}{d x} = \frac{5 x ^{2} + y ^{2}}{x y}

\frac{d y}{d t} + \frac{1}{t} y = \frac{6}{t}, y (1) = 6

\int \frac{sin ( \frac{x}{2} )}{cos ^{2} ( \frac{x}{2} )} d x

f (x) = 2 x - 6

\frac{d}{d t} (e^{t} + e^{- t})

What is (\partial)/(\partial y)(4xln(xy)) ?
The answer to (\partial)/(\partial y)(4xln(xy)) is (4x)/y