derivative (t^2+5)^2-7(t^2+5)

Lösung

ableitung von

(t^{2} + 5)^{2} - 7 (t^{2} + 5)

4 t^{3} + 6 t

Schritte zur Lösung

\frac{d}{d t} ((t^{2} + 5)^{2} - 7 (t^{2} + 5))

Vereinfache

(t^{2} + 5)^{2} - 7 (t^{2} + 5) : t^{4} + 3 t^{2} - 10

= \frac{d}{d t} (t^{4} + 3 t^{2} - 10)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (t^{4}) + \frac{d}{d t} (3 t^{2}) - \frac{d}{d t} (10)

\frac{d}{d t} (t^{4}) = 4 t^{3}

\frac{d}{d t} (3 t^{2}) = 6 t

\frac{d}{d t} (10) = 0

= 4 t^{3} + 6 t - 0

Vereinfache

= 4 t^{3} + 6 t

2 x \frac{d y}{d x} - 8 y = x^{- 8}

a re a \frac{2}{x}, \frac{1}{2} x, 1, 2

\frac{d}{d x} (ln (\frac{2 x - 1}{x - 1}))

\frac{d}{d u} (2 u)

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