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Popular >

derivative of |x^3-x|

Solution

\frac{d}{d x} (x^{3} - x)

Solution

\frac{( x ^{3} - x ) ( 3 x ^{2} - 1 )}{∣ x ^{3} - x ∣}

Solution steps

\frac{d}{d x} (x^{3} - x)

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3} - x) = 3 x^{2} - 1

= \frac{x ^{3} - x}{∣ ( x ^{3} - x ) ∣} (3 x^{2} - 1)

Multiply fractions:

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

= \frac{( x ^{3} - x ) ( 3 x ^{2} - 1 )}{∣ x ^{3} - x ∣}

Popular Examples

integral of 1/5-2/x

\int \frac{1}{5} - \frac{2}{x} d x

(dy)/(dx)=xsqrt(x-18)

\frac{d y}{d x} = x x - 18

laplacetransform-3tsin(2t)laplace transform

- 3 t sin (2 t)

derivative of f(x)=4x^2+2x-3 derivative of

f (x) = 4 x^{2} + 2 x - 3

integral of (cos(2y)-3x^2y^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of |x^3-x| ?
The derivative of |x^3-x| is ((x^3-x)(3x^2-1))/(|x^3-x|)
What is the first derivative of |x^3-x| ?
The first derivative of |x^3-x| is ((x^3-x)(3x^2-1))/(|x^3-x|)