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Beliebt Rechnen >

derivative pi^{x^2}

Lösung

ableitung von

π^{x^{2}}

Lösung

2 ln (π) π^{x^{2}} x

Schritte zur Lösung

\frac{d}{d x} (π^{x^{2}})

Wende Exponentenregel an:

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

π^{x^{2}} = e^{x^{2} l n (π)}

= \frac{d}{d x} (e^{x^{2} l n (π)})

Wende die Kettenregel an:

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

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

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

= e^{x^{2} l n (π)} \cdot 2 ln (π) x

e^{x^{2} l n (π)} = π^{x^{2}}

= 2 ln (π) π^{x^{2}} x

Graph

Beliebte Beispiele

integral of 1/(5-4x)

\int \frac{1}{5 - 4 x} d x

integral of (7-98x)/(sqrt(16-49x^2))

\int \frac{7 - 98 x}{16 - 49 x ^{2}} d x

fläche y=9x,y=x^2-10

a re a y = 9 x, y = x^{2} - 10

integral from 0 to 1 of 3e^{-3t}

\int_{0}^{1} 3 e^{- 3 t} d t

derivative of (3x+1^{1/2})

\frac{d}{d x} ((3 x + 1)^{\frac{1}{2}})