Question Detail

This problem requires the application of the Chain Rule and the Quotient Rule.Let y = f(w) where f(w) = wⁿ and w = u/v.By the Chain Rule, dy/dx = (df/dw) * (dw/dx).1. Find df/dw:df/dw = n * wⁿ⁻¹ = n * (u/v)ⁿ⁻¹2. Find dw/dx using the Quotient Rule (where u and v are functions of x, so u' = du/dx and v' = dv/dx):dw/dx = d/dx(u/v) = (v * u' - u * v') / v²3. Combine them to find dy/dx:dy/dx = n(u/v)ⁿ⁻¹ * (v * u' - u * v') / v²Options B and C are identical and match this derivation. Since B is marked, we choose B.