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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (3 x^{2} - 3) = 6 x

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

= - \frac{1}{2} \cdot \frac{6 xx - 1 \cdot ( 3 x ^{2} - 3 )}{x ^{2}}

Vereinfache

- \frac{1}{2} \cdot \frac{6 xx - 1 \cdot ( 3 x ^{2} - 3 )}{x ^{2}} : - \frac{3 x ^{2} + 3}{2 x ^{2}}

= - \frac{3 x ^{2} + 3}{2 x ^{2}}

\frac{\partial}{\partial x} (8 x^{2})

3 y^{^{''}} - 5 y^{^{'}} - 2 y = x^{3} - 2 x

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

\frac{d}{d x} (arctan (x - 5))

d er i v a t i v e \frac{2 x - 1}{2 x + 3}