derivative f(x)=x^{x^2}

Lösung

ableitung von

f (x) = x^{x^{2}}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

t an g e n t f (x) = 9 x + 4, (5, 7)

\frac{\partial}{\partial v} (\frac{v - u}{2})

x \to + 0 lim (x^{2} \cdot ln (x))

\frac{d}{d x} (12 x^{3} + 4 - ln (3 x + 7))

d er i v a t i v e f (x) = (2 x + 5)^{7}