What is the derivative of sqrt(9x^2-1) ?

The derivative of sqrt(9x^2-1) is (9x)/(sqrt(9x^2-1))

What is the first derivative of sqrt(9x^2-1) ?

The first derivative of sqrt(9x^2-1) is (9x)/(sqrt(9x^2-1))

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derivative of

9 x^{2} - 1

\frac{9 x}{9 x ^{2} - 1}

Solution steps

\frac{d}{d x} (9 x^{2} - 1)

Apply the chain rule:

\frac{1}{2 9 x ^{2} - 1} \frac{d}{d x} (9 x^{2} - 1)

= \frac{1}{2 9 x ^{2} - 1} \frac{d}{d x} (9 x^{2} - 1)

\frac{d}{d x} (9 x^{2} - 1) = 18 x

= \frac{1}{2 9 x ^{2} - 1} \cdot 18 x

Simplify

\frac{1}{2 9 x ^{2} - 1} \cdot 18 x : \frac{9 x}{9 x ^{2} - 1}

= \frac{9 x}{9 x ^{2} - 1}

What is the derivative of sqrt(9x^2-1) ?
The derivative of sqrt(9x^2-1) is (9x)/(sqrt(9x^2-1))
What is the first derivative of sqrt(9x^2-1) ?
The first derivative of sqrt(9x^2-1) is (9x)/(sqrt(9x^2-1))