Question

y= sin^3 4x cos^3 (5x^3 -2)
найти производную... Спасибо заранее

Answer 1

y' = (sin³4x)' * cos³(5x³ - 2) + sin³4x * (cos³(5x³ - 2))' = 3sin²4x*(sin4x)' * cos³(5x³ - 2) + sin³4x * 3cos²(5x³ - 2)*(cos(5x³-2))' = 3sin²4x*cos4x*(4x)' * cos³(5x³ - 2) + sin³4x*3cos²(5x³ - 2)*(- sin(5x³ - 2))*(5x³ - 2)' = 3sin²4x*cos4x*4*cos³(5x³ - 2) - sin³4x*3cos²(5x³ - 2)*sin(5x³ - 2)*(15x² - 0) = 12sin²4x*cos4x*cos³(5x³ - 2) - 45sin³4x*cos²(5x³ - 2)*sin(5x³ - 2)*x²