Question Detail
Question
Given that y = e1-2x, evaluate y' at x = 1/2.
Correct Answer
Option B is the correct answer.
Detailed Explanation
To find y', we differentiate y = e1-2x using the chain rule. The derivative of eu is eu * du/dx.Let u = 1 - 2x. Then du/dx = -2.So, y' = e1-2x * (-2) = -2e1-2x.Now, evaluate y' at x = 1/2:y'(1/2) = -2e1-2(1/2) = -2e1-1 = -2e0.Since e0 = 1:y'(1/2) = -2 * 1 = -2.
Hint
Remember the chain rule for differentiating exponential functions: d/dx(ef(x)) = ef(x) * f'(x).