derivative of (2x^{3/2}/x)

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{2 x ^{\frac{3}{2}}}{x} : 2 x^{\frac{1}{2}}

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Vereinfache

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

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

\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))

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