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Popular >

derivative of (1-x^{-1}^{-1})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

y^'=((4+5*y))/6

y^{^{'}} = \frac{( 4 + 5 \cdot y )}{6}

integral of x*x^{1/2}

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

limit as x approaches 0 of (x^2)*ln(x)

x \to 0 lim ((x^{2}) \cdot ln (x))

y^{^{'}} + \frac{1}{x} y = 0

tangent of f(x)=3x^3-3x^2+7,(2,19)tangent of

f (x) = 3 x^{3} - 3 x^{2} + 7, (2, 19)

Frequently Asked Questions (FAQ)

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