What is the derivative of ln(sqrt(x)-1) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

y = \frac{7}{ln ( x )}

\frac{d}{d x} (\frac{5 x}{6})

x \to 9 - lim (\frac{1}{x - 9})

x \to 0 + lim (x [ln (x)]^{2})

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