derivative e^x(x^2+1)(x+4)

Lösung

ableitung von

e^{x} (x^{2} + 1) (x + 4)

e^{x} x^{3} + 7 e^{x} x^{2} + 9 e^{x} x + 5 e^{x}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (x^{2} + 1) (x + 4))

Wende die Produktregel an:

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

f = e^{x}, g = (x^{2} + 1) (x + 4)

= \frac{d}{d x} (e^{x}) (x^{2} + 1) (x + 4) + \frac{d}{d x} ((x^{2} + 1) (x + 4)) e^{x}

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

\frac{d}{d x} ((x^{2} + 1) (x + 4)) = 3 x^{2} + 8 x + 1

= e^{x} (x^{2} + 1) (x + 4) + (3 x^{2} + 8 x + 1) e^{x}

Vereinfache

e^{x} (x^{2} + 1) (x + 4) + (3 x^{2} + 8 x + 1) e^{x} : e^{x} x^{3} + 7 e^{x} x^{2} + 9 e^{x} x + 5 e^{x}

= e^{x} x^{3} + 7 e^{x} x^{2} + 9 e^{x} x + 5 e^{x}

a re a y = - x, y = - x^{2} + e x

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