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

Lösung

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

\frac{x ^{2} - 1}{x x}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{x ^{2} - 1}{x x}

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

\int \frac{sin ( 2 x )}{( 1 + cos ( 2 x ) ) ^{3}} d x

d er i v a t i v e f (x) = \frac{x ^{5}}{5} + \frac{1}{12 x ^{3}}

t an g e n t y = sin (2 x) + sin (2) (2 x)

x \to - \frac{π}{2} lim (2 tan (x))