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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x y^{^{'}} = y + x e^{\frac{y}{x}}

\int_{- 4}^{2} - x^{2} - 2 x + 8 d x

t an g e n t y = sin (7 x) + sin^{2} (7 x), (0, 0)

\int_{0}^{1} ∣ 2 x - 1 ∣ d x

\int_{0}^{2 π} cos (3 t) e^{- 2 t} d t