derivative of (1-x^2^{-2})

Lösung

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

\frac{4 x}{( 1 - x ^{2} ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{2}{( 1 - x ^{2} ) ^{3}} (- 2 x) : \frac{4 x}{( 1 - x ^{2} ) ^{3}}

= \frac{4 x}{( 1 - x ^{2} ) ^{3}}

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial x} (x^{y^{x}})

\int \frac{1}{x ^{2} + 64} d x

t an g e n t y = 2 x^{3} - x^{2} + 2

\int \frac{e ^{x^{n}}}{x ^{1 - n}} d x