derivative of (x^4+3/(6x))

Lösung

\frac{d}{d x} (\frac{x ^{4} + 3}{6 x})

\frac{x ^{4} - 1}{2 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{4} + 3}{6 x})

Entferne die Konstante:

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

= \frac{1}{6} \frac{d}{d x} (\frac{x ^{4} + 3}{x})

Wende die Quotientenregel an:

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

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( x ^{4} + 3 ) x - \frac{d x}{d x} ( x ^{4} + 3 )}{x ^{2}}

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

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

= \frac{1}{6} \cdot \frac{4 x ^{3} x - 1 \cdot ( x ^{4} + 3 )}{x ^{2}}

Vereinfache

\frac{1}{6} \cdot \frac{4 x ^{3} x - 1 \cdot ( x ^{4} + 3 )}{x ^{2}} : \frac{x ^{4} - 1}{2 x ^{2}}

= \frac{x ^{4} - 1}{2 x ^{2}}

\frac{d}{d y} (3 y)

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

a re a f (y) = 2 x, 0, 4

\frac{d}{d x} (arctan (sin (2 x)))

\int 1 - 4 (\frac{1}{2} sin (x))^{2} d x