derivative 4ln(9-5x^2)

Lösung

ableitung von

4 ln (9 - 5 x^{2})

- \frac{40 x}{9 - 5 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (4 ln (9 - 5 x^{2}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (ln (9 - 5 x^{2}))

Wende die Kettenregel an:

\frac{1}{9 - 5 x ^{2}} \frac{d}{d x} (9 - 5 x^{2})

= \frac{1}{9 - 5 x ^{2}} \frac{d}{d x} (9 - 5 x^{2})

\frac{d}{d x} (9 - 5 x^{2}) = - 10 x

= 4 \cdot \frac{1}{9 - 5 x ^{2}} (- 10 x)

Vereinfache

4 \cdot \frac{1}{9 - 5 x ^{2}} (- 10 x) : - \frac{40 x}{9 - 5 x ^{2}}

= - \frac{40 x}{9 - 5 x ^{2}}

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