(\partial)/(\partial x)(2(y/x)^{1/2})

Lösung

\frac{\partial}{\partial x} (2 (\frac{y}{x})^{\frac{1}{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (2 (\frac{y}{x})^{\frac{1}{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} ((\frac{y}{x})^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( \frac{y}{x} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{y}{x})

= \frac{1}{2 ( \frac{y}{x} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{y}{x})

\frac{\partial}{\partial x} (\frac{y}{x}) = - \frac{y}{x ^{2}}

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

Vereinfache

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

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

d er i v a t i v e f (x) = 3 x + 3

n = 1 \sum \infty \frac{x ^{n}}{n \cdot 5 n}

\frac{d}{d x} ((x^{3} - 16 x)^{10})

\frac{d}{d t} (1 + t)

\frac{d y}{d t} = 2 t + y + 1