derivative of 1/(x^4-3/(x^2)+x^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

\frac{d}{d x} (\frac{3}{x ^{2}}) = - \frac{6}{x ^{3}}

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

= - \frac{4}{x ^{5}} - (- \frac{6}{x ^{3}}) + 3 x^{2}

Vereinfache

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

\int \frac{1}{2 x ^{2} + 3} d x

v \to 3 lim (\frac{v + 1 - 2}{v - 3})

x \to 3 lim (\frac{x - 2}{x ^{2} - 9})

\int \frac{1}{x ^{2} + 4 x + 5} d x

t an g e n t f (x) = \frac{9}{x - 3}, at x = 2