derivative of (4e^{4x}/(e^8(e^{16)-1)})

Lösung

\frac{d}{d x} (\frac{4 e ^{4 x}}{e ^{8} ( e ^{16} - 1 )})

\frac{16 e ^{4 x - 8}}{e ^{16} - 1}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 e ^{4 x}}{e ^{8} ( e ^{16} - 1 )})

Entferne die Konstante:

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

= \frac{4}{e ^{8} ( e ^{16} - 1 )} \frac{d}{d x} (e^{4 x})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (4 x) = 4

= \frac{4}{e ^{8} ( e ^{16} - 1 )} e^{4 x} \cdot 4

Vereinfache

\frac{4}{e ^{8} ( e ^{16} - 1 )} e^{4 x} \cdot 4 : \frac{16 e ^{4 x - 8}}{e ^{16} - 1}

= \frac{16 e ^{4 x - 8}}{e ^{16} - 1}

t an g e n t y = sin (x), at x = \frac{5 π}{3}

x \to 0 lim (\frac{5 ^{x} - 7 ^{x}}{x})

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