derivative of 2x^3+(5x+1/(3x-5)-2/(x^3))

Lösung

\frac{d}{d x} (2 x^{3} + \frac{5 x + 1}{3 x - 5} - \frac{2}{x ^{3}})

6 x^{2} - \frac{28}{( 3 x - 5 ) ^{2}} + \frac{6}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{3} + \frac{5 x + 1}{3 x - 5} - \frac{2}{x ^{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (\frac{5 x + 1}{3 x - 5}) - \frac{d}{d x} (\frac{2}{x ^{3}})

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

\frac{d}{d x} (\frac{5 x + 1}{3 x - 5}) = - \frac{28}{( 3 x - 5 ) ^{2}}

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

= 6 x^{2} - \frac{28}{( 3 x - 5 ) ^{2}} - (- \frac{6}{x ^{4}})

Vereinfache

= 6 x^{2} - \frac{28}{( 3 x - 5 ) ^{2}} + \frac{6}{x ^{4}}

\frac{d}{d x} (\frac{1}{12} (x + 2)^{3} + (x + 2)^{- 1})

x \to 0 lim (\frac{7 ^{x} - 9 ^{x}}{x})

d er i v a t i v e g (t) = 4 t^{- \frac{1}{8}}

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

\int_{(- 2)}^{8} (∣ x - 2 ∣ - 3) d x