derivative of |x^3+3x^2-24x-80|

Lösung

\frac{d}{d x} (x^{3} + 3 x^{2} - 24 x - 80)

\frac{( x ^{3} + 3 x ^{2} - 24 x - 80 ) ( 3 x ^{2} + 6 x - 24 )}{∣ x ^{3} + 3 x ^{2} - 24 x - 80 ∣}

Schritte zur Lösung

\frac{d}{d x} (x^{3} + 3 x^{2} - 24 x - 80)

Wende die Kettenregel an:

\frac{x ^{3} + 3 x ^{2} - 24 x - 80}{∣ ( x ^{3} + 3 x ^{2} - 24 x - 80 ) ∣} \frac{d}{d x} (x^{3} + 3 x^{2} - 24 x - 80)

= \frac{x ^{3} + 3 x ^{2} - 24 x - 80}{∣ ( x ^{3} + 3 x ^{2} - 24 x - 80 ) ∣} \frac{d}{d x} (x^{3} + 3 x^{2} - 24 x - 80)

\frac{d}{d x} (x^{3} + 3 x^{2} - 24 x - 80) = 3 x^{2} + 6 x - 24

= \frac{x ^{3} + 3 x ^{2} - 24 x - 80}{∣ ( x ^{3} + 3 x ^{2} - 24 x - 80 ) ∣} (3 x^{2} + 6 x - 24)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( x ^{3} + 3 x ^{2} - 24 x - 80 ) ( 3 x ^{2} + 6 x - 24 )}{∣ x ^{3} + 3 x ^{2} - 24 x - 80 ∣}

\frac{d}{d x} (\frac{3 sin ( x )}{3 + cos ( x )})

im pl i c i t \frac{d y}{d x}, e^{x y} + x^{2} - y^{2} = 12

n = 0 \sum \infty (\frac{1}{17})^{n}

x \to 0 lim (\frac{sin ( 5 x )}{6 x})

d er i v a t i v e f (x) = 3 sec (5 x)