derivative (t^2-2t)(t^2+2t)

Lösung

ableitung von

(t^{2} - 2 t) (t^{2} + 2 t)

4 t^{3} - 8 t

Schritte zur Lösung

\frac{d}{d t} ((t^{2} - 2 t) (t^{2} + 2 t))

Wende die Produktregel an:

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

f = t^{2} - 2 t, g = t^{2} + 2 t

= \frac{d}{d t} (t^{2} - 2 t) (t^{2} + 2 t) + \frac{d}{d t} (t^{2} + 2 t) (t^{2} - 2 t)

\frac{d}{d t} (t^{2} - 2 t) = 2 t - 2

\frac{d}{d t} (t^{2} + 2 t) = 2 t + 2

= (2 t - 2) (t^{2} + 2 t) + (2 t + 2) (t^{2} - 2 t)

Vereinfache

(2 t - 2) (t^{2} + 2 t) + (2 t + 2) (t^{2} - 2 t) : 4 t^{3} - 8 t

= 4 t^{3} - 8 t

\frac{\partial}{\partial x} (9 y^{4} cos (x^{2}))

d er i v a t i v e f (x) = \frac{1}{x ^{2} - 9}

in v erse l a pl a ce \frac{1}{2}

\int x^{2} \cdot e^{- 3 x} d x

\frac{\partial}{\partial x} (- ln (x))