What is the derivative of |x^3+3x^2-24x-80| ?

The derivative of |x^3+3x^2-24x-80| is ((x^3+3x^2-24x-80)(3x^2+6x-24))/(|x^3+3x^2-24x-80|)

What is the first derivative of |x^3+3x^2-24x-80| ?

The first derivative of |x^3+3x^2-24x-80| is ((x^3+3x^2-24x-80)(3x^2+6x-24))/(|x^3+3x^2-24x-80|)

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\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 ∣}

Solution steps

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

Apply the chain rule:

\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)

Multiply fractions:

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 ∣}

What is the derivative of |x^3+3x^2-24x-80| ?
The derivative of |x^3+3x^2-24x-80| is ((x^3+3x^2-24x-80)(3x^2+6x-24))/(|x^3+3x^2-24x-80|)
What is the first derivative of |x^3+3x^2-24x-80| ?
The first derivative of |x^3+3x^2-24x-80| is ((x^3+3x^2-24x-80)(3x^2+6x-24))/(|x^3+3x^2-24x-80|)