derivative of (x^2-8x+4/(2x))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 8 x + 4}{2 x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 8 x + 4}{2 x})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (\frac{x ^{2} - 8 x + 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} - 8 x + 4 ) x - \frac{d x}{d x} ( x ^{2} - 8 x + 4 )}{x ^{2}}

\frac{d}{d x} (x^{2} - 8 x + 4) = 2 x - 8

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

= \frac{1}{2} \cdot \frac{( 2 x - 8 ) x - 1 \cdot ( x ^{2} - 8 x + 4 )}{x ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{( 2 x - 8 ) x - 1 \cdot ( x ^{2} - 8 x + 4 )}{x ^{2}} : \frac{x ^{2} - 4}{2 x ^{2}}

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

d er i v a t i v e (1 + 7 x^{2}) (x - x^{2})

\int_{0}^{\frac{π}{4}} tan^{2} (x) d x

\int \frac{3 x ^{2}}{125} d x

d er i v a t i v e sin (cos (tan (x)))

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