derivative 4^{(x^9)}

Lösung

ableitung von

4^{(x^{9})}

9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

Schritte zur Lösung

\frac{d}{d x} (4^{x^{9}})

Wende Exponentenregel an:

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

4^{x^{9}} = e^{x^{9} l n (4)}

= \frac{d}{d x} (e^{x^{9} l n (4)})

Wende die Kettenregel an:

e^{x^{9} l n (4)} \frac{d}{d x} (x^{9} ln (4))

= e^{x^{9} l n (4)} \frac{d}{d x} (x^{9} ln (4))

\frac{d}{d x} (x^{9} ln (4)) = 18 ln (2) x^{8}

= e^{x^{9} l n (4)} \cdot 18 ln (2) x^{8}

Vereinfache

e^{x^{9} l n (4)} \cdot 18 ln (2) x^{8} : 9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

= 9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

t a y l or \frac{1}{( 2 + x ) ^{3}}

x \to - \infty lim (3^{- x})

s l o p e (\frac{11}{6}, - \frac{1}{2}), (\frac{1}{3}, \frac{1}{3})

s l o p e (1) (3.5)

\int 19 arctan (x) d x