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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{x - 2} \cdot \frac{1}{2 x - 2} : \frac{1}{2 ( x - 2 )}

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

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