What is the derivative of log_{e}(x-1) ?

The derivative of log_{e}(x-1) is 1/(x-1)

What is the first derivative of log_{e}(x-1) ?

The first derivative of log_{e}(x-1) is 1/(x-1)

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\frac{d}{d x} (lo g_{e} (x - 1))

\frac{1}{x - 1}

Solution steps

\frac{d}{d x} (lo g_{e} (x - 1))

Simplify

lo g_{e} (x - 1) : ln (x - 1)

= \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) = 1

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

Simplify

= \frac{1}{x - 1}

\frac{d}{d x} (\frac{1}{4 + x})

\frac{d}{d x} ((4 x - 9) ln ((2 x - 5) (x - 2)))

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

\int 10 (x - 6)^{4} d x

\int \frac{1}{x ^{2} - x - 2} d x

What is the derivative of log_{e}(x-1) ?
The derivative of log_{e}(x-1) is 1/(x-1)
What is the first derivative of log_{e}(x-1) ?
The first derivative of log_{e}(x-1) is 1/(x-1)