derivative of-((x^3+x-1/2))

Lösung

\frac{d}{d x} (- (\frac{x ^{3} + x - 1}{2}))

- \frac{1}{2} (3 x^{2} + 1)

Schritte zur Lösung

\frac{d}{d x} (- (\frac{x ^{3} + x - 1}{2}))

Entferne die Konstante:

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

= - \frac{1}{2} \frac{d}{d x} (x^{3} + x - 1)

Wende die Summen-/Differenzregel an:

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

= - \frac{1}{2} (\frac{d}{d x} (x^{3}) + \frac{d x}{d x} - \frac{d}{d x} (1))

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

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

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

= - \frac{1}{2} (3 x^{2} + 1 - 0)

Vereinfache

= - \frac{1}{2} (3 x^{2} + 1)

d er i v a t i v e f (x) = \frac{7}{x} - x

\frac{d}{d x} (1 + 2 x)

d er i v a t i v e (\frac{5 x - 1}{4 x + 2})^{- 5}

x \to 0 - lim (1 - e^{x})

\int_{0}^{3} (10 x - 6 x^{2} + 9) d x