derivative of 8^{x^8}

Lösung

\frac{d}{d x} (8^{x^{8}})

3 ln (2) \cdot 2^{3 x^{8} + 3} x^{7}

Schritte zur Lösung

\frac{d}{d x} (8^{x^{8}})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

8^{x^{8}} = e^{x^{8} l n (8)}

= \frac{d}{d x} (e^{x^{8} l n (8)})

Wende die Kettenregel an:

e^{x^{8} l n (8)} \frac{d}{d x} (x^{8} ln (8))

= e^{x^{8} l n (8)} \frac{d}{d x} (x^{8} ln (8))

\frac{d}{d x} (x^{8} ln (8)) = 24 ln (2) x^{7}

= e^{x^{8} l n (8)} \cdot 24 ln (2) x^{7}

Vereinfache

e^{x^{8} l n (8)} \cdot 24 ln (2) x^{7} : 3 ln (2) \cdot 2^{3 x^{8} + 3} x^{7}

= 3 ln (2) \cdot 2^{3 x^{8} + 3} x^{7}

\int (\frac{2}{x} + 2 x) d x

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

\int e^{- 0.4 x} d x

x \to - 2 lim (\frac{x + 2}{x ^{3} + 8})

z \to 2 lim (6 z - 1)