derivative f(x)= 1/x+1/(x^2)+1/(x^3)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

\frac{d}{d x} (2 lo g_{10} (x) - 3 x)

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

d er i v a t i v e \frac{3 x + 4}{3 x - 4}

x (y + 1) d x + y (x - 1) d y = 0

x \to 0 lim (\frac{x}{x ^{2} - 1})