derivative of 1/(sqrt(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{2}{1 + x ^{4}} d x

d er i v a t i v e \frac{1}{6 x}

\int e^{t y} (4 y + 1) d y

\int e^{2 x} \cdot sin (x) d x

t an g e n t f (x) = \frac{1}{6} x^{4}, at x = - 1