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

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

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

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

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

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

Solution steps

\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}{e ^{x} 1 - e ^{2 x}} d x

f (x) = sin^{2} (\frac{x}{2})

x \cdot \frac{d y}{d x} + (11 + x) y = e^{- x}

\int_{0}^{x^{2}} sin (t) d t

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

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