d/(dn)(n^n)

Lösung

\frac{d}{d n} (n^{n})

n^{n} (ln (n) + 1)

Schritte zur Lösung

\frac{d}{d n} (n^{n})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d n} (n ln (n)) = ln (n) + 1

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

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

= n^{n} (ln (n) + 1)

\frac{d r}{d θ} = \frac{r ^{2} + 2 r θ}{θ ^{2}}

x \to 1 lim (e^{x - 1} + 1)

n or ma l y = 4 x^{2} + 3 y^{2} + 8 x - 6 y - 45, (- 2, - 3)

x \to + 1 lim (x^{2} + x - 3)

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