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

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

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

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

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derivative of

\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}}

x \cdot y^{^{'}} = x^{2} - 2 x y - y^{2} + y

\int 3 x 2 x^{2} + 1 d x

\frac{\partial}{\partial y} (4 z e^{x yz})

x \to - 9 - lim (\frac{- 6 x}{x + 9})

\frac{d}{d x} (\frac{x + 3}{x ^{2} + 3})

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