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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

- \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}}

Vereinfache

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

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

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

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

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

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

t an g e n t f (x) = 3 x^{3} - 3 x^{2} + 7, (2, 19)