What is the derivative of y= 1/(x-1) ?

The derivative of y= 1/(x-1) is -1/((x-1)^2)

What is the first derivative of y= 1/(x-1) ?

The first derivative of y= 1/(x-1) is -1/((x-1)^2)

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derivative of

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{1}{2 + x} d x

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\int_{6}^{10} ln (x^{13}) d x

What is the derivative of y= 1/(x-1) ?
The derivative of y= 1/(x-1) is -1/((x-1)^2)
What is the first derivative of y= 1/(x-1) ?
The first derivative of y= 1/(x-1) is -1/((x-1)^2)