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

Lösung

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

\frac{1}{4}

Dezimale

0.25

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{1}{4}

\int_{1}^{2} \frac{1}{x ^{8}} d x

n = 1 \sum \infty \frac{2}{( n + 2 ) ^{3}}

\frac{d}{d x} (e^{3 x - 3})

\frac{d}{d x} y = 5 x^{2} cos^{2} (y)

t an g e n t f (x) = 2 x cos (x), at x = \frac{3 π}{2}