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

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

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

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

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

\frac{1}{2 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x}

\int cos (x) (2 + 5 sin^{2} (x)) d x

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\int \frac{7}{25 - x ^{2}} d x

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