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Beliebt Rechnen >

derivative f(x)=pi^{x^2}

Lösung

ableitung von

f (x) = 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

y^{^{'}} = 2

integral of 8x^{-5}

\int 8 x^{- 5} d x

integral of 1/(sqrt(x^2+100))

\int \frac{1}{x ^{2} + 100} d x

ty^'=2y+2t^3sin(3t),y(pi/3)=0

t y^{^{'}} = 2 y + 2 t^{3} sin (3 t), y (\frac{π}{3}) = 0

integral of (e^{\sqrt[5]{t}})/(sqrt(t))

\int \frac{e ^{5 t}}{t} d t