What is the derivative of sqrt(x^3-4x) ?

The derivative of sqrt(x^3-4x) is (3x^2-4)/(2sqrt(x^3-4x))

What is the first derivative of sqrt(x^3-4x) ?

The first derivative of sqrt(x^3-4x) is (3x^2-4)/(2sqrt(x^3-4x))

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derivative of

x^{3} - 4 x

\frac{3 x ^{2} - 4}{2 x ^{3} - 4 x}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{3} - 4 x} \frac{d}{d x} (x^{3} - 4 x)

= \frac{1}{2 x ^{3} - 4 x} \frac{d}{d x} (x^{3} - 4 x)

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

= \frac{1}{2 x ^{3} - 4 x} (3 x^{2} - 4)

Simplify

\frac{1}{2 x ^{3} - 4 x} (3 x^{2} - 4) : \frac{3 x ^{2} - 4}{2 x ^{3} - 4 x}

= \frac{3 x ^{2} - 4}{2 x ^{3} - 4 x}

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