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

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

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

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

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

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

Solution steps

\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}{2 x}

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

Simplify

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

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

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