f(x) = x (1-2x)^3

1. find the derivative

f '(x) = (1 -2x)^3 + x (3) (1 -2x)^2 (-2)

f '(x) = (1 -2x)^3 - 6x (1 -2x)^2 [Product Rule]

2. You are looking for the tan. line at (1, -1) so you plug in x =1 into this equation

f ' (-1) = -7

3. Use the formula to find equ ofa line

y - y1 = m (x - x1)

y - (-1) = (-7) (x -1)

y + 1 = -7x + 7

y = -7x +6

y = tan(x) - cot (x)

y' = (sec(x))^2 + (csc(x))^2

Hope this Helps.