derivative of 2x^7-7x^{-4}+2x^2-3x

Lösung

\frac{d}{d x} (2 x^{7} - 7 x^{- 4} + 2 x^{2} - 3 x)

14 x^{6} + \frac{28}{x ^{5}} + 4 x - 3

Schritte zur Lösung

\frac{d}{d x} (2 x^{7} - 7 x^{- 4} + 2 x^{2} - 3 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{7}) - \frac{d}{d x} (7 x^{- 4}) + \frac{d}{d x} (2 x^{2}) - \frac{d}{d x} (3 x)

\frac{d}{d x} (2 x^{7}) = 14 x^{6}

\frac{d}{d x} (7 x^{- 4}) = - \frac{28}{x ^{5}}

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

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

= 14 x^{6} - (- \frac{28}{x ^{5}}) + 4 x - 3

Vereinfache

= 14 x^{6} + \frac{28}{x ^{5}} + 4 x - 3

x \to \infty lim (\frac{x + 3}{2 x ^{3} - 5})

d er i v a t i v e 3^{x} ln (3)

\int_{1}^{2} 4 r^{2} ln (r) d r

\frac{d}{d x} (\frac{- 9}{4 x})

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