derivative (5x^2-8x)e^x

Lösung

ableitung von

(5 x^{2} - 8 x) e^{x}

5 e^{x} x^{2} + 2 e^{x} x - 8 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{2} - 8 x) e^{x})

Wende die Produktregel an:

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

f = 5 x^{2} - 8 x, g = e^{x}

= \frac{d}{d x} (5 x^{2} - 8 x) e^{x} + \frac{d}{d x} (e^{x}) (5 x^{2} - 8 x)

\frac{d}{d x} (5 x^{2} - 8 x) = 10 x - 8

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

= (10 x - 8) e^{x} + e^{x} (5 x^{2} - 8 x)

Vereinfache

(10 x - 8) e^{x} + e^{x} (5 x^{2} - 8 x) : 5 e^{x} x^{2} + 2 e^{x} x - 8 e^{x}

= 5 e^{x} x^{2} + 2 e^{x} x - 8 e^{x}

\int \frac{1}{1 - 4 x ^{2}} d x

t an g e n t f (x) = - 5 - 3 x^{2}, - 53, at x = 4

s l o p e (- 3.2) (7.6)

\int x^{2} (x^{3} - 1)^{10} d x

x \to - 3 lim (\frac{7}{x ^{7}})