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

The derivative of (ln(x^2))/2 is 1/x

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

The first derivative of (ln(x^2))/2 is 1/x

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derivative of

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

\frac{1}{x}

Solution steps

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

Take the constant out:

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

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

Simplify

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

= \frac{1}{x}

What is the derivative of (ln(x^2))/2 ?
The derivative of (ln(x^2))/2 is 1/x
What is the first derivative of (ln(x^2))/2 ?
The first derivative of (ln(x^2))/2 is 1/x