Verified answer

6) y = Sin(π - 4x) = - Sin4x

y' = (- Sin4x)' = - Cos4x * (4x)' = - 4Cos4x

y'(x₀) = - 4Cos(4 * π/3) = - 4Cos(4π/3) = - 4Cos(π + π/3) = 4Cosπ/3= 4 * 1/2 = 2

7) tgα = y'(x₀)

y' = [(1+2x²)' * x - (1 + 2x²) * x'] / x² = [4x * x - (1 + 2x²)] / x² =

= (4x² - 1 - 2x²) / x² = (2x² - 1) /x²

y'(x₀) = y*(2) = (2 * 2² - 1) / 2² = 7/4 = 1,75

tgα = 1,75