What is the derivative of |3x^3+5x| ?

The derivative of |3x^3+5x| is ((3x^3+5x)(9x^2+5))/(|3x^3+5x|)

What is the first derivative of |3x^3+5x| ?

The first derivative of |3x^3+5x| is ((3x^3+5x)(9x^2+5))/(|3x^3+5x|)

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\frac{d}{d x} (3 x^{3} + 5 x)

\frac{( 3 x ^{3} + 5 x ) ( 9 x ^{2} + 5 )}{∣ 3 x ^{3} + 5 x ∣}

Solution steps

\frac{d}{d x} (3 x^{3} + 5 x)

Apply the chain rule:

\frac{3 x ^{3} + 5 x}{∣ ( 3 x ^{3} + 5 x ) ∣} \frac{d}{d x} (3 x^{3} + 5 x)

= \frac{3 x ^{3} + 5 x}{∣ ( 3 x ^{3} + 5 x ) ∣} \frac{d}{d x} (3 x^{3} + 5 x)

\frac{d}{d x} (3 x^{3} + 5 x) = 9 x^{2} + 5

= \frac{3 x ^{3} + 5 x}{∣ ( 3 x ^{3} + 5 x ) ∣} (9 x^{2} + 5)

Multiply fractions:

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

= \frac{( 3 x ^{3} + 5 x ) ( 9 x ^{2} + 5 )}{∣ 3 x ^{3} + 5 x ∣}

\frac{\partial}{\partial x} (x y - ln (z))

\int e^{x + y} d y

\frac{\partial}{\partial s} (\frac{s ^{2} + 4}{t - 3})

x \to 0 - lim (\frac{2 x}{∣ x ∣})

t y^{^{''}} - y^{^{'}} = t^{2} + t, y (1) = 1, y^{^{'}} (1) = 5

What is the derivative of |3x^3+5x| ?
The derivative of |3x^3+5x| is ((3x^3+5x)(9x^2+5))/(|3x^3+5x|)
What is the first derivative of |3x^3+5x| ?
The first derivative of |3x^3+5x| is ((3x^3+5x)(9x^2+5))/(|3x^3+5x|)