derivative of x^{ex}

Lösung

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

e x^{e x} (ln (x) + 1)

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (e x ln (x)) = e (ln (x) + 1)

= e^{e x l n (x)} e (ln (x) + 1)

Vereinfache

e^{e x l n (x)} e (ln (x) + 1) : e x^{e x} (ln (x) + 1)

= e x^{e x} (ln (x) + 1)

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

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

d er i v a t i v e f (x) = (2 x^{2} + 1)

\int x^{2} sin (y) d y

\int sin (6 x) ln (sin (6 x)) d x