Derivative of xsqrt1-x^2

1. Differentiate $- x^{2} + \sqrt{1} x$ term by term:

   1. 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: $\sqrt{1}$

   2. 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: $- 2 x$

   The result is: $- 2 x + \sqrt{1}$

2. Now simplify:

   $$1 - 2 x$$

The answer is:

$$1 - 2 x$$