derivative of ln((5x^2+9^3))

Lösung

\frac{d}{d x} (ln ((5 x^{2} + 9)^{3}))

\frac{30 x}{5 x ^{2} + 9}

Schritte zur Lösung

\frac{d}{d x} (ln ((5 x^{2} + 9)^{3}))

Wende die Kettenregel an:

\frac{1}{( 5 x ^{2} + 9 ) ^{3}} \frac{d}{d x} ((5 x^{2} + 9)^{3})

= \frac{1}{( 5 x ^{2} + 9 ) ^{3}} \frac{d}{d x} ((5 x^{2} + 9)^{3})

\frac{d}{d x} ((5 x^{2} + 9)^{3}) = 30 x (5 x^{2} + 9)^{2}

= \frac{1}{( 5 x ^{2} + 9 ) ^{3}} \cdot 30 x (5 x^{2} + 9)^{2}

Vereinfache

\frac{1}{( 5 x ^{2} + 9 ) ^{3}} \cdot 30 x (5 x^{2} + 9)^{2} : \frac{30 x}{5 x ^{2} + 9}

= \frac{30 x}{5 x ^{2} + 9}

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