derivative of 1/(x^7+2)

Lösung

\frac{d}{d x} (\frac{1}{x ^{7} + 2})

- \frac{7 x ^{6}}{( x ^{7} + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{7} + 2})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{7} + 2)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{7} + 2 ) ^{2}} \frac{d}{d x} (x^{7} + 2)

= - \frac{1}{( x ^{7} + 2 ) ^{2}} \frac{d}{d x} (x^{7} + 2)

\frac{d}{d x} (x^{7} + 2) = 7 x^{6}

= - \frac{1}{( x ^{7} + 2 ) ^{2}} \cdot 7 x^{6}

Vereinfache

- \frac{1}{( x ^{7} + 2 ) ^{2}} \cdot 7 x^{6} : - \frac{7 x ^{6}}{( x ^{7} + 2 ) ^{2}}

= - \frac{7 x ^{6}}{( x ^{7} + 2 ) ^{2}}

\frac{\partial}{\partial x} (x^{2} + 2 x y)

\int 3 e^{x} sin (3 x) d x

\frac{\partial}{\partial x} (sin (x) + y)

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

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