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Beliebt Rechnen >

derivative of log_{3}((x^2+2x^4))

Lösung

\frac{d}{d x} (lo g_{3} ((x^{2} + 2 x)^{4}))

Lösung

\frac{4 ( 2 x + 2 )}{ln ( 3 ) ( x ^{2} + 2 x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} ((x^{2} + 2 x)^{4}))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} \frac{ln ( ( x ^{2} + 2 x ) ^{4} )}{ln ( 3 )}

Entferne die Konstante:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln ((x^{2} + 2 x)^{4}))

Wende die Kettenregel an:

\frac{1}{( x ^{2} + 2 x ) ^{4}} \frac{d}{d x} ((x^{2} + 2 x)^{4})

= \frac{1}{( x ^{2} + 2 x ) ^{4}} \frac{d}{d x} ((x^{2} + 2 x)^{4})

\frac{d}{d x} ((x^{2} + 2 x)^{4}) = 4 (x^{2} + 2 x)^{3} (2 x + 2)

= \frac{1}{ln ( 3 )} \cdot \frac{1}{( x ^{2} + 2 x ) ^{4}} \cdot 4 (x^{2} + 2 x)^{3} (2 x + 2)

Vereinfache

\frac{1}{ln ( 3 )} \cdot \frac{1}{( x ^{2} + 2 x ) ^{4}} \cdot 4 (x^{2} + 2 x)^{3} (2 x + 2) : \frac{4 ( 2 x + 2 )}{ln ( 3 ) ( x ^{2} + 2 x )}

= \frac{4 ( 2 x + 2 )}{ln ( 3 ) ( x ^{2} + 2 x )}

Graph

Beliebte Beispiele

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