Объяснение:
1) f ' (x) = 4x^3 - 15x^2
2) f ' (x) = 3/4*8x^7 + 3(-2)*x^(-3) - 1/6*1/(2√x) = 6x^7 - 6/x^3 + 1/(12√x)
3) f ' (x) = 13/3*3x^2 - 1x^(-2) = 13x^2 - 1/x^2
4) f ' (x) = 1(x+1) + (x-5)*1 = 2x - 4
5) f ' (x) = [2(x-4) - (2x+5)*1] / (x-4)^2 = (2x-8-2x-5)/(x-4)^2 = -13/(x-4)^2
6) f ' (x) = 2x(3x-7) + (x^2-1)*3 = 6x^2-14x+3x^2-3 = 9x^2 - 14x - 3
7) f ' (x) = [(3x^2-4)*x - (x^3-4x+3)*1] / x^2 = (3x^3-4x-x^3+4x-3)/x^2 = (2x^3 - 3)/x^2
8) f ' (x) = 1/(2√(8+4x))*4 = 2/√(8+4x)
9) f ' (x) = 1/(2√(3x^2-8x))*(6x-8) = (3x-4)/√(3x^2-8x)
10) f ' (x) = 1*√(3-4x) + x/(2√(3-4x))*(-4) = √(3-4x) - 2x/√(3-4x)
Объяснение:
1) f ' (x) = 4x^3 - 15x^2
2) f ' (x) = 3/4*8x^7 + 3(-2)*x^(-3) - 1/6*1/(2√x) = 6x^7 - 6/x^3 + 1/(12√x)
3) f ' (x) = 13/3*3x^2 - 1x^(-2) = 13x^2 - 1/x^2
4) f ' (x) = 1(x+1) + (x-5)*1 = 2x - 4
5) f ' (x) = [2(x-4) - (2x+5)*1] / (x-4)^2 = (2x-8-2x-5)/(x-4)^2 = -13/(x-4)^2
6) f ' (x) = 2x(3x-7) + (x^2-1)*3 = 6x^2-14x+3x^2-3 = 9x^2 - 14x - 3
7) f ' (x) = [(3x^2-4)*x - (x^3-4x+3)*1] / x^2 = (3x^3-4x-x^3+4x-3)/x^2 = (2x^3 - 3)/x^2
8) f ' (x) = 1/(2√(8+4x))*4 = 2/√(8+4x)
9) f ' (x) = 1/(2√(3x^2-8x))*(6x-8) = (3x-4)/√(3x^2-8x)
10) f ' (x) = 1*√(3-4x) + x/(2√(3-4x))*(-4) = √(3-4x) - 2x/√(3-4x)