What is (\partial)/(\partial y)(ln(xy^2)) ?

The answer to (\partial)/(\partial y)(ln(xy^2)) is 2/y

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(\partial)/(\partial y)(ln(xy^2))

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

\frac{2}{y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x y ^{2}} \frac{\partial}{\partial y} (x y^{2})

= \frac{1}{x y ^{2}} \frac{\partial}{\partial y} (x y^{2})

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

= \frac{1}{x y ^{2}} \cdot 2 x y

Simplify

\frac{1}{x y ^{2}} \cdot 2 x y : \frac{2}{y}

= \frac{2}{y}

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What is (\partial)/(\partial y)(ln(xy^2)) ?
The answer to (\partial)/(\partial y)(ln(xy^2)) is 2/y