Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 25

You need to use the product and chain rules to evaluate the derivative of the function, such that:
f'(x) = (x)'(sqrt(1 - x^2)) + (x)(sqrt(1 - x^2))'
f'(x) = (sqrt(1 - x^2)) + (x)((-2x)/(2sqrt(1 - x^2)))
f'(x) = (sqrt(1 - x^2)) - (x^2)/(sqrt(1 - x^2)))
Hence, evaluating the derivative of the function, using the product rule, yields f'(x) = (sqrt(1 - x^2)) - (x^2)/(sqrt(1 - x^2))).