derivative f(x)=(x^2-1)/2

Lösung

ableitung von

f (x) = \frac{x ^{2} - 1}{2}

x

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{2} (2 x - 0)

Vereinfache

\frac{1}{2} (2 x - 0) : x

= x

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