derivative of (3x+2/(4x))

Lösung

\frac{d}{d x} (\frac{3 x + 2}{4 x})

- \frac{1}{2 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 2}{4 x})

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (\frac{3 x + 2}{x})

Wende die Quotientenregel an:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 3 x + 2 ) x - \frac{d x}{d x} ( 3 x + 2 )}{x ^{2}}

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

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

= \frac{1}{4} \cdot \frac{3 x - 1 \cdot ( 3 x + 2 )}{x ^{2}}

Vereinfache

\frac{1}{4} \cdot \frac{3 x - 1 \cdot ( 3 x + 2 )}{x ^{2}} : - \frac{1}{2 x ^{2}}

= - \frac{1}{2 x ^{2}}

\frac{d}{d x} (- sin (7 x^{2}) \cdot 14 x)

\frac{d x}{d t} + 2 t x = t, x (0) = \frac{3}{2}

t an g e n t f (x) = 5 x^{3} + 4 x, at x = - 3

f (x) = x \cdot cos (x)

\frac{d}{d x} (((x^{2} + 3)^{5} + x)^{2})