derivative of 1/((a^2+x^2^{n/2)})

Lösung

\frac{d}{d x} (\frac{1}{( a ^{2} + x ^{2} ) ^{\frac{n}{2}}})

- n x (a^{2} + x^{2})^{- \frac{n}{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( a ^{2} + x ^{2} ) ^{\frac{n}{2}}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((a^{2} + x^{2})^{- \frac{n}{2}})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int t^{3} ln (t) d t

\int sin (m x) sin (n x) d x

d er i v a t i v e y = \frac{8 x ^{2} + 2 x + 6}{x}

\frac{d}{d x} (1000 x e^{- 0.5 x})

\frac{\partial}{\partial x} (z^{3} ln (x y))