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

Lösung

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

\frac{x ^{\frac{5}{2}} - 4 + 6 x ^{5}}{2 x ^{\frac{5}{2}} x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

Vereinfache

\frac{1}{2 x} - \frac{2}{x ^{3}} + 3 x^{2} : \frac{x ^{\frac{5}{2}} - 4 + 6 x ^{5}}{2 x ^{\frac{5}{2}} x}

= \frac{x ^{\frac{5}{2}} - 4 + 6 x ^{5}}{2 x ^{\frac{5}{2}} x}

x \to 5 lim (5 + x^{4})

\int e^{- s t} (t) d t

\int \frac{x ^{\frac{3}{2}} + 2 x ^{6} + 1.2}{x} d x

d er i v a t i v e cos (arctan (3 x) - arcsin (2 x))

\frac{d}{d x} (6 \cdot 5^{x})