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Beliebt Rechnen >

derivative of a^{x^2}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

integral of ((ln(x))^2)/x

\int \frac{( ln ( x ) ) ^{2}}{x} d x

derivative (3x^2-1)^4

d er i v a t i v e (3 x^{2} - 1)^{4}

integral from-1 to 3 of (x^3-2x)

\int_{- 1}^{3} (x^{3} - 2 x) d x

integral of (x^2cos(x)-2xcos(x))

\int (x^{2} cos (x) - 2 x cos (x)) d x

derivative f(x)=(x^3)(e^x)

d er i v a t i v e f (x) = (x^{3}) (e^{x})