derivative (x^4)/2-3/2 x^2-x

Lösung

ableitung von

\frac{x ^{4}}{2} - \frac{3}{2} x^{2} - x

x (2 x^{2} - 3) - 1

Schritte zur Lösung

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

Vereinfache

\frac{x ^{4}}{2} - \frac{3}{2} x^{2} - x : \frac{x ^{4} - 3 x ^{2}}{2} - x

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d x}{d x} = 1

= x (2 x^{2} - 3) - 1