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Beliebt Rechnen >

derivative f(x)=((x+7)/(x+9))^6

Lösung

ableitung von

f (x) = (\frac{x + 7}{x + 9})^{6}

Lösung

\frac{12 ( x + 7 ) ^{5}}{( x + 9 ) ^{7}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 7}{x + 9})^{6})

Wende die Kettenregel an:

6 (\frac{x + 7}{x + 9})^{5} \frac{d}{d x} (\frac{x + 7}{x + 9})

= 6 (\frac{x + 7}{x + 9})^{5} \frac{d}{d x} (\frac{x + 7}{x + 9})

\frac{d}{d x} (\frac{x + 7}{x + 9}) = \frac{2}{( x + 9 ) ^{2}}

= 6 (\frac{x + 7}{x + 9})^{5} \frac{2}{( x + 9 ) ^{2}}

Vereinfache

6 (\frac{x + 7}{x + 9})^{5} \frac{2}{( x + 9 ) ^{2}} : \frac{12 ( x + 7 ) ^{5}}{( x + 9 ) ^{7}}

= \frac{12 ( x + 7 ) ^{5}}{( x + 9 ) ^{7}}

Graph

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