derivative of-24e^{-8x^3}x^2

Lösung

\frac{d}{d x} (- 24 e^{- 8 x^{3}} x^{2})

- 24 (- 24 e^{- 8 x^{3}} x^{4} + 2 e^{- 8 x^{3}} x)

Schritte zur Lösung

\frac{d}{d x} (- 24 e^{- 8 x^{3}} x^{2})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 24 \frac{d}{d x} (e^{- 8 x^{3}} x^{2})

Wende die Produktregel an:

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

f = e^{- 8 x^{3}}, g = x^{2}

= - 24 (\frac{d}{d x} (e^{- 8 x^{3}}) x^{2} + \frac{d}{d x} (x^{2}) e^{- 8 x^{3}})

\frac{d}{d x} (e^{- 8 x^{3}}) = - 24 e^{- 8 x^{3}} x^{2}

\frac{d}{d x} (x^{2}) = 2 x

= - 24 ((- 24 e^{- 8 x^{3}} x^{2}) x^{2} + 2 x e^{- 8 x^{3}})

Vereinfache

- 24 ((- 24 e^{- 8 x^{3}} x^{2}) x^{2} + 2 x e^{- 8 x^{3}}) : - 24 (- 24 e^{- 8 x^{3}} x^{4} + 2 e^{- 8 x^{3}} x)

= - 24 (- 24 e^{- 8 x^{3}} x^{4} + 2 e^{- 8 x^{3}} x)

\frac{d}{d x} (x^{2} - 2 x)

\frac{d}{d x} (cos (x) + x \cdot sin (x))

d er i v a t i v e f (x) = (x^{3} + 8) e^{x}

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

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