derivative of 1/(2sqrt(x)+1/(6x^{5/6)})

Lösung

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}})

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{5}{36 x ^{\frac{11}{6}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}})

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}{6 x ^{\frac{5}{6}}})

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

\frac{d}{d x} (\frac{1}{6 x ^{\frac{5}{6}}}) = - \frac{5}{36 x ^{\frac{11}{6}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{5}{36 x ^{\frac{11}{6}}}

\frac{\partial}{\partial x} (\frac{y + x y}{( 1 + x ) ^{3}})

\frac{d}{d x} (e^{5 x} \cdot 5)

d er i v a t i v e u + 1 (1 - 8 u^{2})^{7}

d er i v a t i v e e^{- b t}

x \to - 2 - lim (\frac{1 - x}{x ^{3} + 8})