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

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

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

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

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

\frac{ln ( x )}{x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= \frac{1}{2} \cdot 2 ln (x) \frac{1}{x}

Simplify

\frac{1}{2} \cdot 2 ln (x) \frac{1}{x} : \frac{ln ( x )}{x}

= \frac{ln ( x )}{x}

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