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

Lösung

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

x - \frac{3}{2}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

\frac{1}{2} (2 x - 3) : x - \frac{3}{2}

= x - \frac{3}{2}

t an g e n t f (x) = 3 x^{2} - x^{3}, at x = 1

\frac{d}{d x} (- 3 sin (x) - 2)

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

t an g e n t f (x) = 11 + 9 x - x^{3}, at x = 1

\frac{d}{d x} (\frac{3 x - 3}{x - 3})