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Beliebt Rechnen >

derivative f(x)=e^{x+1}-3e^x+2e^{x^3}

Lösung

ableitung von

f (x) = e^{x + 1} - 3 e^{x} + 2 e^{x^{3}}

Lösung

e^{x + 1} - 3 e^{x} + 6 e^{x^{3}} x^{2}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (e^{x + 1}) = e^{x + 1}

\frac{d}{d x} (3 e^{x}) = 3 e^{x}

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

= e^{x + 1} - 3 e^{x} + 6 e^{x^{3}} x^{2}

Graph

Beliebte Beispiele

integral from 2 to infinity of 2x^{-2}

\int_{2}^{\infty} 2 x^{- 2} d x

integral of 1/(3+2y)

\int \frac{1}{3 + 2 y} d y

integral of (1/y)

\int (\frac{1}{y}) d y

integral from 0 to 9 of piy^3

\int_{0}^{9} π y^{3} d y

fläche x^3-10x,6x,[-4,4]

a re a x^{3} - 10 x, 6 x, [- 4, 4]