derivative of (3x/(x-2))

Lösung

\frac{d}{d x} (\frac{3 x}{x - 2})

- \frac{6}{( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x}{x - 2})

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

= 3 \cdot \frac{\frac{d x}{d x} ( x - 2 ) - \frac{d}{d x} ( x - 2 ) x}{( x - 2 ) ^{2}}

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

\frac{d}{d x} (x - 2) = 1

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

Vereinfache

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

= - \frac{6}{( x - 2 ) ^{2}}

\int_{2}^{4} (x^{2} + 2)^{3} x d x

\int (a - x)^{3} d x

\frac{\partial}{\partial x} (ln (2 x) + 5 y^{3})

\frac{\partial}{\partial y} (ln (x + \frac{y}{2 x}))

y^{^{'}} = - 10 y