1. The problem is to simplify the expression for the derivative: $$f'(x) = - \frac{(1+x)^2}{1-x} \cdot \frac{1+x}{1+x}$$ 2. Notice that multiplying by \(\frac{1+x}{1+x}\) is multiplying by 1, so it does not change the value but helps in simplification. 3. Combine the numerators and denominators: $$f'(x) = - \frac{(1+x)^2 \cdot (1+x)}{(1-x) \cdot (1+x)}$$ 4. Simplify the numerator: $$ (1+x)^2 \cdot (1+x) = (1+x)^3 $$ 5. Simplify the denominator: $$ (1-x) \cdot (1+x) = 1 - x^2 $$ 6. So the expression becomes: $$f'(x) = - \frac{(1+x)^3}{1 - x^2}$$ 7. This is the simplified form of the derivative. Final answer: $$f'(x) = - \frac{(1+x)^3}{1 - x^2}$$