Derivative of sqrt(1-3x^2)

1. Let $u = 1 - 3 x^{2}$.

2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - 3 x^{2}\right)$:

   1. Differentiate $1 - 3 x^{2}$ term by term:

      1. The derivative of the constant $1$ is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

         1. The derivative of a constant times a function is the constant times the derivative of the function.

            1. Apply the power rule: $x^{2}$ goes to $2 x$

            So, the result is: $6 x$

         So, the result is: $- 6 x$

      The result is: $- 6 x$

   The result of the chain rule is:

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

4. Now simplify:

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

The answer is: