derivative (x^3+4)e^x

Lösung

ableitung von

(x^{3} + 4) e^{x}

3 x^{2} e^{x} + e^{x} (x^{3} + 4)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 4) e^{x})

Wende die Produktregel an:

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

f = x^{3} + 4, g = e^{x}

= \frac{d}{d x} (x^{3} + 4) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 4)

\frac{d}{d x} (x^{3} + 4) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 4)

t an g e n t f (x) = (1 - x) (x^{2} - 3) 2

x \to - 1 lim (x^{3})

\frac{\partial}{\partial x} (7 y)

\int_{1}^{5} (6 - x) - (8 - 3 x) d x

\frac{\partial}{\partial y} (x e^{- y})