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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{2}{sin ^{2} ( + 2 )}

y^{^{''}} + y = sec (x) tan (x)

f (x) = x

x \to 0 lim (cos (π x))

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