Question

Найдите производные след функций y=18 y=x y=19x y=x^8 y=3x^5+5 y=3/7x^7+3/5x^5+2/3x^3+3 y=(4x^2-3)(4x^2-1) y=5x/(x^2+3)

Answer 1

1) y' = 0
2) y' = 1
3) y' = 19
4) y' = 8x^7
5) y' = 15x^4
6) y' = 3x^6 + 3x^4 + 2x^2
7) y' = (4x^2-3)'(4x^2-1)+(4x^2-3)(4x^2-1)' = 8x(4x^2-1)+8x(4x^2-3) = 32x^3-8x+32x^3 - 24x = 64x^3-16x
8) y' = ((5x)'(x^2+3)-5x(x^2+3)')/(x^2+3)^2 = (5x^2+15-10x^2-15x)/(x^2+3)^2 = (-5x^2-15x+15)/(x^2+3)^2