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

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

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

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

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derivative of

y = 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}

y = ln (x^{2})

f (x) = x + 9

y = x^{3}

(- \frac{9 3}{2}, \frac{9}{2})

x 1 - x^{2}

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