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

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

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

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

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

\frac{1}{2 ( 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 - 1}

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

Simplify

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

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

\int_{- 2}^{7} \frac{d}{d t} ((t - 7) (1 - t)) d t

\int_{0}^{0.6} 500 x d x

(8 x^{3} - 5 x + 2)^{π}

\frac{d x}{d t} + x = \frac{1}{t + 1}

\frac{\partial}{\partial x} (cos (2 x + 5 y + 9 z))

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