d/(dm)(c^{im})

Lösung

\frac{d}{d m} (c^{im})

i c^{im} ln (c)

Schritte zur Lösung

\frac{d}{d m} (c^{im})

Behandle

i, c

als Konstante

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d m} (im ln (c)) = i ln (c)

= e^{im l n (c)} i ln (c)

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

= i c^{im} ln (c)

\frac{d}{d x} (5 x^{3} + 2 x^{2} + 6 x + 10)

d er i v a t i v e g (x) = \frac{1}{5 x ^{2} + 3 x}

x \to \infty lim (x^{- 7})

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

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