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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{\partial ^{2}}{\partial y ^{2}} (sin^{2} (m x + n y))

\int \frac{x ^{2}}{4 x ^{2} + 9} d x

\frac{d}{d x} ((x + 2)^{2})

a re a 3 x^{2}, x^{3}

\frac{\partial}{\partial x} (e^{7 x + 3 y})