d/(dn)(i^{2n+3})

Lösung

\frac{d}{d n} (i^{2 n + 3})

2 ln (i) i^{2 n + 3}

Schritte zur Lösung

\frac{d}{d n} (i^{2 n + 3})

Wende Exponentenregel an:

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

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

= \frac{d}{d n} (e^{(2 n + 3) l n (i)})

Wende die Kettenregel an:

e^{(2 n + 3) l n (i)} \frac{d}{d n} ((2 n + 3) ln (i))

= e^{(2 n + 3) l n (i)} \frac{d}{d n} ((2 n + 3) ln (i))

\frac{d}{d n} ((2 n + 3) ln (i)) = 2 ln (i)

= e^{(2 n + 3) l n (i)} \cdot 2 ln (i)

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

= 2 ln (i) i^{2 n + 3}

d er i v a t i v e y = \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + \frac{x}{4}

d er i v a t i v e y = ln ((x + 3)^{2})

d er i v a t i v e \frac{2 x y}{( x ^{2} + y ^{2} )}

d er i v a t i v e \frac{1}{( 1 - t ^{2} )}

d er i v a t i v e 5 e^{3} x