derivative f(x)=e^{x^3ln(x)}

Lösung

ableitung von

f (x) = e^{x^{3} l n (x)}

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

Schritte zur Lösung

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

Vereinfache

e^{x^{3} l n (x)} : x^{x^{3}}

= \frac{d}{d x} (x^{x^{3}})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

d er i v a t i v e f (x) = \frac{6}{3 x + 1}

d er i v a t i v e f (x) = 8 - 2 x

\frac{\partial}{\partial y} (e^{4 x y})

n = 0 \sum \infty (\frac{e}{10})^{n}

t an g e n t f (x) = x^{2} - 1, at x = - 1