What is the derivative of |2x^3+4x-2| ?

The derivative of |2x^3+4x-2| is ((2x^3+4x-2)(6x^2+4))/(|2x^3+4x-2|)

What is the first derivative of |2x^3+4x-2| ?

The first derivative of |2x^3+4x-2| is ((2x^3+4x-2)(6x^2+4))/(|2x^3+4x-2|)

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

\frac{( 2 x ^{3} + 4 x - 2 ) ( 6 x ^{2} + 4 )}{∣ 2 x ^{3} + 4 x - 2 ∣}

Solution steps

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

Apply the chain rule:

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

= \frac{2 x ^{3} + 4 x - 2}{∣ ( 2 x ^{3} + 4 x - 2 ) ∣} \frac{d}{d x} (2 x^{3} + 4 x - 2)

\frac{d}{d x} (2 x^{3} + 4 x - 2) = 6 x^{2} + 4

= \frac{2 x ^{3} + 4 x - 2}{∣ ( 2 x ^{3} + 4 x - 2 ) ∣} (6 x^{2} + 4)

Multiply fractions:

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

= \frac{( 2 x ^{3} + 4 x - 2 ) ( 6 x ^{2} + 4 )}{∣ 2 x ^{3} + 4 x - 2 ∣}

4 x^{3} - 16 x

\frac{d x}{d t} - 4 x = cos (4 t)

\int 8 sin (- 2 t + 7) d t

(- 3) (0.1)

f (t) = e^{t} sin (t)

What is the derivative of |2x^3+4x-2| ?
The derivative of |2x^3+4x-2| is ((2x^3+4x-2)(6x^2+4))/(|2x^3+4x-2|)
What is the first derivative of |2x^3+4x-2| ?
The first derivative of |2x^3+4x-2| is ((2x^3+4x-2)(6x^2+4))/(|2x^3+4x-2|)