What is (\partial)/(\partial y)(8xln(xy)) ?

The answer to (\partial)/(\partial y)(8xln(xy)) is (8x)/y

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(\partial)/(\partial y)(8xln(xy))

\frac{\partial}{\partial y} (8 x ln (x y))

\frac{8 x}{y}

Solution steps

\frac{\partial}{\partial y} (8 x ln (x y))

Treat

x

as a constant

Take the constant out:

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

= 8 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

= 8 x \frac{1}{x y} x

Simplify

8 x \frac{1}{x y} x : \frac{8 x}{y}

= \frac{8 x}{y}

t^{2} \cdot y^{^{'}} + t \cdot y = 5

\frac{d}{d x} (e^{x l n (x)})

x \to 0 lim ((e^{x} + x)^{\frac{m}{x}})

\int \frac{7}{9 - 49 x ^{2}} d x

{\frac{1}{s ^{4}}}

What is (\partial)/(\partial y)(8xln(xy)) ?
The answer to (\partial)/(\partial y)(8xln(xy)) is (8x)/y