derivative f(x)=(x^3+8)e^x

Lösung

ableitung von

f (x) = (x^{3} + 8) e^{x}

3 x^{2} e^{x} + e^{x} (x^{3} + 8)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 8) e^{x})

Wende die Produktregel an:

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

f = x^{3} + 8, g = e^{x}

= \frac{d}{d x} (x^{3} + 8) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 8)

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

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

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

s l o p e y = \frac{16}{( x + 4 ) ^{2}}, (0, 1)

x \to 2 lim (\frac{1}{3.9})

a re a y = tan (x), y = - 3 tan (x), x = \frac{π}{4}

x \to 0 lim (\frac{9 ^{x} - 1 3 ^{x}}{x})

t an g e n t (8 x - x^{2}) (1.7)