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Beliebt Rechnen >

derivative f(x)=log_{10}(x^8+9)

Lösung

ableitung von

f (x) = lo g_{10} (x^{8} + 9)

Lösung

\frac{8 x ^{7}}{ln ( 10 ) ( x ^{8} + 9 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (x^{8} + 9))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( x ^{8} + 9 )}{ln ( 10 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{8} + 9))

Wende die Kettenregel an:

\frac{1}{x ^{8} + 9} \frac{d}{d x} (x^{8} + 9)

= \frac{1}{x ^{8} + 9} \frac{d}{d x} (x^{8} + 9)

\frac{d}{d x} (x^{8} + 9) = 8 x^{7}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{8} + 9} \cdot 8 x^{7}

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{8} + 9} \cdot 8 x^{7} : \frac{8 x ^{7}}{ln ( 10 ) ( x ^{8} + 9 )}

= \frac{8 x ^{7}}{ln ( 10 ) ( x ^{8} + 9 )}

Graph

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