(\partial)/(\partial x)(5sqrt(y/x))

Lösung

\frac{\partial}{\partial x} (5 \frac{y}{x})

- \frac{5 y}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial x} (5 \frac{y}{x})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 5 \frac{\partial}{\partial x} (\frac{y}{x})

Wende die Kettenregel an:

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

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

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

= 5 \cdot \frac{1}{2 \frac{y}{x}} (- \frac{y}{x ^{2}})

Vereinfache

5 \cdot \frac{1}{2 \frac{y}{x}} (- \frac{y}{x ^{2}}) : - \frac{5 y}{2 x ^{\frac{3}{2}}}

= - \frac{5 y}{2 x ^{\frac{3}{2}}}

x \to 0 - lim (\frac{x}{3 x ^{4} - 15 x})

t an g e n t f (x) = (1 - x) (x^{2} - 3) 2, (2, - 1)

\int_{0}^{π} π (3 sin^{2} (x))^{2} d x

\frac{\partial}{\partial z} (e^{x y} \cdot sin (z))

x \to 0 lim (\frac{3}{x ^{3}})