derivative-6t(5t^3-1)^7

Lösung

ableitung von

- 6 t (5 t^{3} - 1)^{7}

- 6 ((5 t^{3} - 1)^{7} + 105 t^{3} (5 t^{3} - 1)^{6})

Schritte zur Lösung

\frac{d}{d t} (- 6 t (5 t^{3} - 1)^{7})

Entferne die Konstante:

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

= - 6 \frac{d}{d t} (t (5 t^{3} - 1)^{7})

Wende die Produktregel an:

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

f = t, g = (5 t^{3} - 1)^{7}

= - 6 (\frac{d t}{d t} (5 t^{3} - 1)^{7} + \frac{d}{d t} ((5 t^{3} - 1)^{7}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} ((5 t^{3} - 1)^{7}) = 105 t^{2} (5 t^{3} - 1)^{6}

= - 6 (1 \cdot (5 t^{3} - 1)^{7} + 105 t^{2} (5 t^{3} - 1)^{6} t)

Vereinfache

- 6 (1 \cdot (5 t^{3} - 1)^{7} + 105 t^{2} (5 t^{3} - 1)^{6} t) : - 6 ((5 t^{3} - 1)^{7} + 105 t^{3} (5 t^{3} - 1)^{6})

= - 6 ((5 t^{3} - 1)^{7} + 105 t^{3} (5 t^{3} - 1)^{6})

x \to - 3 lim (x^{2} - 5)

x \to 2 - lim (\frac{2 x}{x - 2})

x \to c + lim (g (x))

\frac{d}{d x} (\frac{( 1 - 4 x )}{1 + 4 x})

\frac{d}{d x} (e^{x^{3} + 1})