What is the derivative of ln(x^2) ?

The derivative of ln(x^2) is 2/x

What is the first derivative of ln(x^2) ?

The first derivative of ln(x^2) is 2/x

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

\frac{2}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{x}

What is the derivative of ln(x^2) ?
The derivative of ln(x^2) is 2/x
What is the first derivative of ln(x^2) ?
The first derivative of ln(x^2) is 2/x