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

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

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

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

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derivative of

ln (x)

\frac{1}{2 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x}

\int e^{- x} 1 + \frac{1}{e ^{2 x}} d x

arccot (8 y)

\frac{\partial}{\partial x} (x^{3} + y^{3} + z^{3})

\frac{d}{d x} (2 + ∣ x - 3 ∣)

\int \frac{7}{x - 6} d x

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