derivative of 2/(sqrt(x)-(sqrt(3x))/3)

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{2}{x} - \frac{3 x}{3} : \frac{2}{x} - \frac{x}{3}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= - \frac{1}{x ^{\frac{3}{2}}} - \frac{1}{2 3 x}

\frac{d}{d x} (\frac{x ^{3}}{4} + \frac{1}{3 x})

\int 2 d x

x \to 1 lim ([5 f (x) + g (x)])

\frac{d}{d x} (ln (e x))

\int \frac{2 x}{x ^{2} x ^{4} - 1} d x