derivative of 1/2 x^4-4x^2+4

Lösung

\frac{d}{d x} (\frac{1}{2} x^{4} - 4 x^{2} + 4)

2 x^{3} - 8 x

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} x^{4} - 4 x^{2} + 4)

Vereinfache

\frac{1}{2} x^{4} - 4 x^{2} + 4 : \frac{x ^{4}}{2} - 4 x^{2} + 4

= \frac{d}{d x} (\frac{x ^{4}}{2} - 4 x^{2} + 4)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{4}}{2}) - \frac{d}{d x} (4 x^{2}) + \frac{d}{d x} (4)

\frac{d}{d x} (\frac{x ^{4}}{2}) = 2 x^{3}

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (4) = 0

= 2 x^{3} - 8 x + 0

Vereinfache

= 2 x^{3} - 8 x

\frac{\partial}{\partial z} (x z - 7 yz + 4)

\int e^{- s t} cos (2 t) d t

d er i v a t i v e x^{2} + 3

d er i v a t i v e 2 x^{3} 25 - x^{2}

x \to 0 + lim (1)