(\partial)/(\partial x)((e*x)/(c-x))

Lösung

\frac{\partial}{\partial x} (\frac{e \cdot x}{c - x})

\frac{ec}{( c - x ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{e x}{c - x})

Entferne die Konstante:

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

= e \frac{\partial}{\partial x} (\frac{x}{c - x})

Wende die Quotientenregel an:

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

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

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

\frac{\partial}{\partial x} (c - x) = - 1

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

Vereinfache

e \frac{1 \cdot ( c - x ) - ( - 1 ) x}{( c - x ) ^{2}} : \frac{ec}{( c - x ) ^{2}}

= \frac{ec}{( c - x ) ^{2}}

x \to 4 - lim (\frac{- 2}{x ^{2} - 16})

d er i v a t i v e 2 x^{2} - 3

\int \frac{1}{25 x ^{2} - 4} d x

\frac{d}{d x} (\frac{1}{2} x^{3} + \frac{1}{6 x})

\frac{\partial}{\partial x} (3^{4} - 6 5^{3})