derivative of (3x^2-9^{-15})

Lösung

\frac{d}{d x} ((3 x^{2} - 9)^{- 15})

- \frac{10 x}{4782969 ( x ^{2} - 3 ) ^{16}}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 9)^{- 15})

Wende die Kettenregel an:

- \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \frac{d}{d x} (3 x^{2} - 9)

= - \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \frac{d}{d x} (3 x^{2} - 9)

\frac{d}{d x} (3 x^{2} - 9) = 6 x

= - \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \cdot 6 x

Vereinfache

- \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \cdot 6 x : - \frac{10 x}{4782969 ( x ^{2} - 3 ) ^{16}}

= - \frac{10 x}{4782969 ( x ^{2} - 3 ) ^{16}}

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