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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

Vereinfache

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

\int_{1}^{e} \frac{- 2 ln ( x )}{x ^{2}} d x

\int \frac{x}{1 + sin ( x )} d x

t an g e n t f (x) = \frac{1}{5} x^{10} - \frac{1}{3} x^{6} - x + 9

\int \frac{2 y}{( 2 + 3 y ^{2} ) ^{3}} d y

\frac{d y}{d t} = y - y^{2}