derivative of |x^3+10x^2+25x|

Lösung

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\frac{( x ^{3} + 10 x ^{2} + 25 x ) ( 3 x ^{2} + 20 x + 25 )}{∣ x ^{3} + 10 x ^{2} + 25 x ∣}

Schritte zur Lösung

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

Wende die Kettenregel an:

\frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} \frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

= \frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} \frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x) = 3 x^{2} + 20 x + 25

= \frac{x ^{3} + 10 x ^{2} + 25 x}{∣ ( x ^{3} + 10 x ^{2} + 25 x ) ∣} (3 x^{2} + 20 x + 25)

Multipliziere Brüche:

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

= \frac{( x ^{3} + 10 x ^{2} + 25 x ) ( 3 x ^{2} + 20 x + 25 )}{∣ x ^{3} + 10 x ^{2} + 25 x ∣}

\int_{0}^{1} \frac{x}{4 - x ^{2}} d x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 5 y = 0

\frac{d}{d x} (\frac{sin ^{2} ( x )}{cos ^{2} ( x )})

\int x^{a} d x

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