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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - 1) = 6 x

= \frac{1}{2 3 x ^{2} - 1} \cdot 6 x

Simplify

\frac{1}{2 3 x ^{2} - 1} \cdot 6 x : \frac{3 x}{3 x ^{2} - 1}

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

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