What is the first d/(dy)(ln(y^2)) ?

The first d/(dy)(ln(y^2)) is 2/y

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d/(dy)(ln(y^2))

\frac{d}{d y} (ln (y^{2}))

\frac{2}{y}

Solution steps

\frac{d}{d y} (ln (y^{2}))

Apply the chain rule:

\frac{1}{y ^{2}} \frac{d}{d y} (y^{2})

= \frac{1}{y ^{2}} \frac{d}{d y} (y^{2})

\frac{d}{d y} (y^{2}) = 2 y

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

Simplify

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

= \frac{2}{y}