Question

Найдите производную функции


составьте уравнение касательной к графику

Answer 1

y' = -((3x)'cosx + (cosx)'3x) = -(3cosx -3xsinx) = 3x sinx - 3cosx

y' = (3x - 2x^2)'(5x - 1) - (5x - 1)'(3x -2x^2)/(5x - 1)^2 = (3 - 4x)(5x - 1) - 15x + 10x^2/(5x - 1)^2 = -20x^2 + 19x - 3 - 15x+10x^2 /

(5x-1)^2 = -10x^2 + 4x -3/(5x-1)^2

y' = ((2x^4 - x)^5)' = 5(2x^4 - x)^4 × (8x^3 -1) = (40x^3 - 5)(2x^4 - x)^4