What is the derivative of |x^3+3x^2-8| ?

The derivative of |x^3+3x^2-8| is ((x^3+3x^2-8)(3x^2+6x))/(|x^3+3x^2-8|)

What is the first derivative of |x^3+3x^2-8| ?

The first derivative of |x^3+3x^2-8| is ((x^3+3x^2-8)(3x^2+6x))/(|x^3+3x^2-8|)

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\frac{d}{d x} (x^{3} + 3 x^{2} - 8)

\frac{( x ^{3} + 3 x ^{2} - 8 ) ( 3 x ^{2} + 6 x )}{∣ x ^{3} + 3 x ^{2} - 8 ∣}

Solution steps

\frac{d}{d x} (x^{3} + 3 x^{2} - 8)

Apply the chain rule:

\frac{x ^{3} + 3 x ^{2} - 8}{∣ ( x ^{3} + 3 x ^{2} - 8 ) ∣} \frac{d}{d x} (x^{3} + 3 x^{2} - 8)

= \frac{x ^{3} + 3 x ^{2} - 8}{∣ ( x ^{3} + 3 x ^{2} - 8 ) ∣} \frac{d}{d x} (x^{3} + 3 x^{2} - 8)

\frac{d}{d x} (x^{3} + 3 x^{2} - 8) = 3 x^{2} + 6 x

= \frac{x ^{3} + 3 x ^{2} - 8}{∣ ( x ^{3} + 3 x ^{2} - 8 ) ∣} (3 x^{2} + 6 x)

Multiply fractions:

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

= \frac{( x ^{3} + 3 x ^{2} - 8 ) ( 3 x ^{2} + 6 x )}{∣ x ^{3} + 3 x ^{2} - 8 ∣}

\int 3 cos^{3} (2 x) d x

e^{x} cos (x)

\frac{d}{d t} (2)

f (x) = (- 9 x^{3} + 2 x^{2})^{5}

\int e^{x} \cdot 2 d x

What is the derivative of |x^3+3x^2-8| ?
The derivative of |x^3+3x^2-8| is ((x^3+3x^2-8)(3x^2+6x))/(|x^3+3x^2-8|)
What is the first derivative of |x^3+3x^2-8| ?
The first derivative of |x^3+3x^2-8| is ((x^3+3x^2-8)(3x^2+6x))/(|x^3+3x^2-8|)