Final answer:
The derivative of the function \(\sqrt{1+x / 1-x}\) with respect to x involves rewriting the function with fractional exponents and applying the chain rule along with the quotient rule to find the derivative.
Step-by-step explanation:
The question asks for the derivative of the function \(\sqrt{1+x / 1-x}\) with respect to x. To find the derivative, we can rewrite the function using the fact that the square root function is the same as raising to the power of 1/2, so the function becomes \((1+x / 1-x)^{1/2}\). We then apply the chain rule, first by taking the derivative of the outer function u^{1/2} with respect to u, which is 1/2u^{-1/2}, then by finding the derivative of the inner function 1+x / 1-x with respect to x, which requires the quotient rule. Combining these derivatives gives the final result.