derivative of (2x^2-6^{-10})

Lösung

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

- \frac{5 x}{256 ( x ^{2} - 3 ) ^{11}}

Schritte zur Lösung

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

Wende die Kettenregel an:

- \frac{10}{( 2 x ^{2} - 6 ) ^{11}} \frac{d}{d x} (2 x^{2} - 6)

= - \frac{10}{( 2 x ^{2} - 6 ) ^{11}} \frac{d}{d x} (2 x^{2} - 6)

\frac{d}{d x} (2 x^{2} - 6) = 4 x

= - \frac{10}{( 2 x ^{2} - 6 ) ^{11}} \cdot 4 x

Vereinfache

- \frac{10}{( 2 x ^{2} - 6 ) ^{11}} \cdot 4 x : - \frac{5 x}{256 ( x ^{2} - 3 ) ^{11}}

= - \frac{5 x}{256 ( x ^{2} - 3 ) ^{11}}

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