1 курс производные есть 1 денек

1)

y = 6x^(1/3)/x^(1/2)

x^(1/3)/x^(1/2) = x^(1/3-1/2) = x^(-1/6)

y'= (6x^(-1/6))' = - x^(-7/6) ;

2)

y = (3x^5-5)^7(5x^3-3)

y' = 7(3x^5-5)^615x^4 (5x^3-3)+

(3x^5-5)^715x^2 = 15x^2(3x^5-5)^6

(7x^2(5x^3-3)+(3x^5-5)) .

Итак,

y' = 15x^2(3x^5-5)^6(7x^2(5x^3-3)+(3x^5-5)) .

y=6x^(-1/6)

y'=6(-1/6)x^(-7/6)= - x^(-7/6).

2. y'=((3x^5-5)^7)'(5x-3)+(3x^5-5)^7(5x-3)'=

7(3x^5-5)^615x^4(5x-3)+15x(3x^5-5)^7=105x^4(5x-3)(3x^5-5)^6+15x(3x^5-5)^7.