derivative of 1/(2sqrt(x)+1/(3x^{2/3)})

Lösung

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

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{2}{9 x ^{\frac{5}{3}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{1}{3 x ^{\frac{2}{3}}}) = - \frac{2}{9 x ^{\frac{5}{3}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{2}{9 x ^{\frac{5}{3}}}

(\frac{2 sin ( x )}{1 - 2 cos ( x )})^{^{'}}

x \to 0 - lim (\frac{9}{x} - \frac{9}{∣ x ∣})

d er i v a t i v e x^{2} (x^{3} + 4) (x^{5} - 6)

\frac{d}{d t} (5 e^{t} sin (t))

d er i v a t i v e 5 x^{4} - 28 x^{3} + 42 x^{2} - 196 x + 49