derivative x^{x^3-2x}

Lösung

ableitung von

x^{x^{3} - 2 x}

x^{x^{3} - 2 x} (ln (x) (3 x^{2} - 2) + x^{2} - 2)

Schritte zur Lösung

\frac{d}{d x} (x^{x^{3} - 2 x})

Wende Exponentenregel an:

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

x^{x^{3} - 2 x} = e^{(x^{3} - 2 x) l n (x)}

= \frac{d}{d x} (e^{(x^{3} - 2 x) l n (x)})

Wende die Kettenregel an:

e^{(x^{3} - 2 x) l n (x)} \frac{d}{d x} ((x^{3} - 2 x) ln (x))

= e^{(x^{3} - 2 x) l n (x)} \frac{d}{d x} ((x^{3} - 2 x) ln (x))

\frac{d}{d x} ((x^{3} - 2 x) ln (x)) = ln (x) (3 x^{2} - 2) + x^{2} - 2

= e^{(x^{3} - 2 x) l n (x)} (ln (x) (3 x^{2} - 2) + x^{2} - 2)

e^{(x^{3} - 2 x) l n (x)} = x^{x^{3} - 2 x}

= x^{x^{3} - 2 x} (ln (x) (3 x^{2} - 2) + x^{2} - 2)

\int x^{2} (3 - 2 x^{3})^{\frac{1}{3}} d x

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

\int_{- 6}^{1} - 2 x^{2} - 10 x + 12 d x

\int ((x - 1)^{2} - (x + 1)^{2}) (x^{3} + 1) d x

\frac{\partial}{\partial x} (z ln (y) + e^{2})