derivative of a^{3x^2}

Lösung

\frac{d}{d x} (a^{3 x^{2}})

6 a^{3 x^{2}} x ln (a)

Schritte zur Lösung

\frac{d}{d x} (a^{3 x^{2}})

Wende Exponentenregel an:

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

a^{3 x^{2}} = e^{3 x^{2} l n (a)}

= \frac{d}{d x} (e^{3 x^{2} l n (a)})

Wende die Kettenregel an:

e^{3 x^{2} l n (a)} \frac{d}{d x} (3 x^{2} ln (a))

= e^{3 x^{2} l n (a)} \frac{d}{d x} (3 x^{2} ln (a))

\frac{d}{d x} (3 x^{2} ln (a)) = 6 x ln (a)

= e^{3 x^{2} l n (a)} \cdot 6 x ln (a)

e^{3 x^{2} l n (a)} = a^{3 x^{2}}

= 6 a^{3 x^{2}} x ln (a)

t a y l or - 4 x^{3} + 3 x^{2} - 6 x + 10

d er i v a t i v e y = x^{3} - 14 x^{2} + 32 x + 4

s \to 0 lim (\frac{- 2 s}{s - 3})

a re a y = - x^{2} + 4, y = 1 - x

\int_{1}^{6} \frac{x ^{2} - 1}{x} d x