derivative 1/((x^2+8)^5)

Lösung

ableitung von

\frac{1}{( x ^{2} + 8 ) ^{5}}

- \frac{10 x}{( x ^{2} + 8 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( x ^{2} + 8 ) ^{5}})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x^{2} + 8)^{- 5})

Wende die Kettenregel an:

- \frac{5}{( x ^{2} + 8 ) ^{6}} \frac{d}{d x} (x^{2} + 8)

= - \frac{5}{( x ^{2} + 8 ) ^{6}} \frac{d}{d x} (x^{2} + 8)

\frac{d}{d x} (x^{2} + 8) = 2 x

= - \frac{5}{( x ^{2} + 8 ) ^{6}} \cdot 2 x

Vereinfache

- \frac{5}{( x ^{2} + 8 ) ^{6}} \cdot 2 x : - \frac{10 x}{( x ^{2} + 8 ) ^{6}}

= - \frac{10 x}{( x ^{2} + 8 ) ^{6}}

\int p (p + 6)^{6} d p

\int 5 \frac{x}{16 - x ^{2}} d x

\int (- 5 x^{4} + 8 x^{3}) (- 2 x^{5} + 4 x^{4})^{6} d x

x \to 2 lim (\frac{( 3 x + 2 )}{5 x - 2})^{\frac{( 3 )}{x - 2}}

x \to \infty lim (x^{6} e^{- x^{5}})