derivative of 4^{(x^9})

Lösung

\frac{d}{d x} (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}

\int (2 x^{2} - 1)^{2} d x

\frac{\partial}{\partial x} (e^{- 2 x} cos (π y))

\int \frac{2 x}{1} d x

n = 0 \sum \infty 1.0 2^{n}

s l o p e in t erce pt (3, - 3), (0, 2)