Derivative of (-1)/sqrt(1-2*x)

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

   1. Let $u = \sqrt{1 - 2 x}$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{1 - 2 x}$:

      1. Let $u = 1 - 2 x$.

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

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

         1. Differentiate $1 - 2 x$ 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. Apply the power rule: $x$ goes to $1$

               So, the result is: $-2$

            The result is: $-2$

         The result of the chain rule is:

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

      The result of the chain rule is:

      $$\frac{1}{\left(1 - 2 x\right)^{\frac{3}{2}}}$$

   So, the result is: $- \frac{1}{\left(1 - 2 x\right)^{\frac{3}{2}}}$

The answer is: