What is the derivative of ln((x^{1/2}/3)) ?

The derivative of ln((x^{1/2}/3)) is 1/(2x)

What is the first derivative of ln((x^{1/2}/3)) ?

The first derivative of ln((x^{1/2}/3)) is 1/(2x)

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\frac{d}{d x} (ln (\frac{x ^{\frac{1}{2}}}{3}))

\frac{1}{2 x}

Solution steps

\frac{d}{d x} (ln (\frac{x ^{\frac{1}{2}}}{3}))

Apply the chain rule:

\frac{1}{\frac{x ^{\frac{1}{2}}}{3}} \frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{3})

= \frac{1}{\frac{x ^{\frac{1}{2}}}{3}} \frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{3})

\frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{3}) = \frac{1}{6 x ^{\frac{1}{2}}}

= \frac{1}{\frac{x ^{\frac{1}{2}}}{3}} \cdot \frac{1}{6 x ^{\frac{1}{2}}}

Simplify

\frac{1}{\frac{x ^{\frac{1}{2}}}{3}} \cdot \frac{1}{6 x ^{\frac{1}{2}}} : \frac{1}{2 x}

= \frac{1}{2 x}

\int (x^{2} - 3) d x

f (x) = ln (x^{3})

3 e^{3 t}

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

\int e^{u} sin (u) d u

What is the derivative of ln((x^{1/2}/3)) ?
The derivative of ln((x^{1/2}/3)) is 1/(2x)
What is the first derivative of ln((x^{1/2}/3)) ?
The first derivative of ln((x^{1/2}/3)) is 1/(2x)