What is the derivative of sqrt(x^3-x) ?

The derivative of sqrt(x^3-x) is (3x^2-1)/(2sqrt(x^3-x))

What is the first derivative of sqrt(x^3-x) ?

The first derivative of sqrt(x^3-x) is (3x^2-1)/(2sqrt(x^3-x))

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derivative of

x^{3} - x

\frac{3 x ^{2} - 1}{2 x ^{3} - x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2} - 1}{2 x ^{3} - x}

\frac{3}{1 - x}

(- 4, - 4), (5, - 7)

y^{^{''}} + 2 y^{^{'}} + y = x^{3}

\int x 5 - x^{2} d x

\int e^{- s t} (3 t) d t

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