derivative f(x)=((e^{4x})/(x^6))^3

Lösung

ableitung von

f (x) = (\frac{e ^{4 x}}{x ^{6}})^{3}

\frac{6 e ^{12 x} ( 2 x - 3 )}{x ^{19}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{e ^{4 x}}{x ^{6}})^{3})

Wende die Kettenregel an:

3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{d}{d x} (\frac{e ^{4 x}}{x ^{6}})

= 3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{d}{d x} (\frac{e ^{4 x}}{x ^{6}})

\frac{d}{d x} (\frac{e ^{4 x}}{x ^{6}}) = \frac{2 e ^{4 x} ( 2 x - 3 )}{x ^{7}}

= 3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{2 e ^{4 x} ( 2 x - 3 )}{x ^{7}}

Vereinfache

3 (\frac{e ^{4 x}}{x ^{6}})^{2} \frac{2 e ^{4 x} ( 2 x - 3 )}{x ^{7}} : \frac{6 e ^{12 x} ( 2 x - 3 )}{x ^{19}}

= \frac{6 e ^{12 x} ( 2 x - 3 )}{x ^{19}}

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