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Beliebt Rechnen >

derivative (x^3+5)e^x

Lösung

ableitung von

(x^{3} + 5) e^{x}

Lösung

3 x^{2} e^{x} + e^{x} (x^{3} + 5)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 5) e^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3} + 5, g = e^{x}

= \frac{d}{d x} (x^{3} + 5) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 5)

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 5)

Graph

Beliebte Beispiele

derivative of iny(x)

\frac{d}{d x} (in y (x))

integral from 1 to 10 of 1/(x^2-4x-32)

\int_{1}^{10} \frac{1}{x ^{2} - 4 x - 32} d x

derivative g(x)= 1/(5x^2+4x)

d er i v a t i v e g (x) = \frac{1}{5 x ^{2} + 4 x}

integral from 3 to infinity of e^{-x/2}

\int_{3}^{\infty} e^{- \frac{x}{2}} d x

derivative of (arctan(4x)^2)

\frac{d}{d x} ((arctan (4 x))^{2})