derivative of (x+1/x ^2-5/(sqrt(3x)))

Lösung

\frac{d}{d x} ((x + \frac{1}{x})^{2} - \frac{5}{3 x})

\frac{- 4 3 x ^{\frac{3}{2}} + 5 x ^{3} + 4 3 x ^{\frac{11}{2}}}{2 3 x ^{\frac{9}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((x + \frac{1}{x})^{2} - \frac{5}{3 x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} ((x + \frac{1}{x})^{2}) - \frac{d}{d x} (\frac{5}{3 x})

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

\frac{d}{d x} (\frac{5}{3 x}) = - \frac{5}{2 3 x ^{\frac{3}{2}}}

= 2 (x + \frac{1}{x}) (1 - \frac{1}{x ^{2}}) - (- \frac{5}{2 3 x ^{\frac{3}{2}}})

Vereinfache

2 (x + \frac{1}{x}) (1 - \frac{1}{x ^{2}}) - (- \frac{5}{2 3 x ^{\frac{3}{2}}}) : \frac{- 4 3 x ^{\frac{3}{2}} + 5 x ^{3} + 4 3 x ^{\frac{11}{2}}}{2 3 x ^{\frac{9}{2}}}

= \frac{- 4 3 x ^{\frac{3}{2}} + 5 x ^{3} + 4 3 x ^{\frac{11}{2}}}{2 3 x ^{\frac{9}{2}}}

\frac{\partial}{\partial x} (x e^{3 y} sin (5 z))

n = 1 \sum \infty (\frac{5}{6})^{n}

d er i v a t i v e y = e^{k t a n (7 x)}

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

d er i v a t i v e y^{\frac{2}{3}}