If y = (1 - 2x)2, find the value of dy/dx at x = -1

Answer Details

To find the derivative of y with respect to x, we need to apply the chain rule and power rule of differentiation. First, we take the derivative of the outer function, which is squaring the quantity (1-2x). This gives us: 2(1-2x) Then, we multiply this result by the derivative of the inner function (1-2x). This gives us: 2(1-2x)(-2) Combining these results, we have: dy/dx = 2(1-2x)(-2) To find the value of dy/dx at x=-1, we substitute -1 for x in the expression above: dy/dx = 2(1-2(-1))(-2) = -54 Therefore, the answer is -54.