derivative of y/(3x)

Lösung

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

\frac{x \frac{d y}{d x} - y}{3 x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} (\frac{y}{x})

Wende die Quotientenregel an:

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

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

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

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

Vereinfache

\frac{1}{3} \cdot \frac{\frac{d y}{d x} x - 1 \cdot y}{x ^{2}} : \frac{x \frac{d y}{d x} - y}{3 x ^{2}}

= \frac{x \frac{d y}{d x} - y}{3 x ^{2}}

\frac{d y}{d x} = - 2 y, y (0) = 3

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

\int 7 sin^{5} (x) cos (x) d x

x \to \infty lim (\frac{3 x - 2}{6 x + 1})

d er i v a t i v e f (x) = arccot (e^{x})