This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Rewrite y using exponential notation. y = (1 - 2x)^(1)/(2) Step 2: Differentiate both sides with respect to x using the chain rule. (dy)/(dx) = (1)/(2)(1 - 2x)^(1)/(2) - 1 · (d)/(dx)(1 - 2x) Step 3: Compute the derivative of the inner function. (d)/(dx)(1 - 2x) = -2 (dy)/(dx) = (1)/(2)(1 - 2x)^-(1)/(2) · (-2) Step 4: Simplify the constants. (dy)/(dx) = (1)/(2) · (-2) · (1 - 2x)^-(1)/(2) (dy)/(dx) = - (1 - 2x)^-(1)/(2) Step 5: Rewrite the negative exponent as a fraction. (dy)/(dx) = -(1)/((1 - 2x)^1)2 Step 6: Rewrite using radical notation. (dy)/(dx) = -(1)/(sqrt(1 - 2x)) (dy)/(dx) = -(1)/(sqrt(1 - 2x))