derivative of 4x^2-11x-5/(x^3)

Lösung

\frac{d}{d x} (4 x^{2} - 11 x - \frac{5}{x ^{3}})

8 x - 11 + \frac{15}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} - 11 x - \frac{5}{x ^{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{2}) - \frac{d}{d x} (11 x) - \frac{d}{d x} (\frac{5}{x ^{3}})

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (11 x) = 11

\frac{d}{d x} (\frac{5}{x ^{3}}) = - \frac{15}{x ^{4}}

= 8 x - 11 - (- \frac{15}{x ^{4}})

Vereinfache

= 8 x - 11 + \frac{15}{x ^{4}}

x \to 0 lim (cos (4 x))

(x^{2} + 1) y^{^{'}} + 4 x (y - 1) = 0

d er i v a t i v e 49 - x^{2}

t a y l or f (x) = x^{3} - 3 x^{2} + 4 x + 5, x = 3

ma c l a u r in (1 + x)^{- \frac{7}{3}}, 4