derivative of (x^3-5x^2-36x/(x^2+4x))

Lösung

\frac{d}{d x} (\frac{x ^{3} - 5 x ^{2} - 36 x}{x ^{2} + 4 x})

1

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} - 5 x ^{2} - 36 x}{x ^{2} + 4 x})

Vereinfache

\frac{x ^{3} - 5 x ^{2} - 36 x}{x ^{2} + 4 x} : x - 9

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (9) = 0

= 1 - 0

Vereinfache

= 1

in v erse l a pl a ce \frac{25}{x ( x ^{2} + 6 x + 25 )}

\frac{d x}{d t} = x - 12

\frac{d}{d x} (sin (\frac{1}{x}) \cdot x^{3})

d er i v a t i v e cos (sin (tan (5 x)))

x \to - 1 lim (x^{3} - 1)