derivative of (x^2+4/(2x))

Lösung

\frac{d}{d x} (\frac{x ^{2} + 4}{2 x})

\frac{x ^{2} - 4}{2 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 4}{2 x})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (\frac{x ^{2} + 4}{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} ( x ^{2} + 4 ) x - \frac{d x}{d x} ( x ^{2} + 4 )}{x ^{2}}

\frac{d}{d x} (x^{2} + 4) = 2 x

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

= \frac{1}{2} \cdot \frac{2 xx - 1 \cdot ( x ^{2} + 4 )}{x ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{2 xx - 1 \cdot ( x ^{2} + 4 )}{x ^{2}} : \frac{x ^{2} - 4}{2 x ^{2}}

= \frac{x ^{2} - 4}{2 x ^{2}}

t an g e n t y = 4 - 2 x^{2}

d er i v a t i v e u + 1

\frac{\partial}{\partial x} (x^{3} + y^{5} + x^{7} - y^{2})

\frac{\partial}{\partial x} (A x)

\frac{d}{d x} (\frac{e ^{- x} cos ^{2} ( x )}{x ^{2} + x + 1})