Question

1 курс производные есть 1 день

Answer 1

y=6·x^(-1/6)

y'=6·(-1/6)x^(-7/6)= - x^(-7/6).

2. y'=((3x^5-5)^7)'·(5x³-3)+(3x^5-5)^7·(5x³-3)'=

7(3x^5-5)^6·15x^4·(5x³-3)+15x²·(3x^5-5)^7=105x^4·(5x³-3)·(3x^5-5)^6+15x²·(3x^5-5)^7.

Answer 2

1)

y = 6×x^(1/3)/x^(1/2)

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

y'= (6×x^(-1/6))' = - x^(-7/6) ;

2)

y = (3x^5-5)^7×(5x^3-3)

y' = 7(3x^5-5)^6×15x^4× (5x^3-3)+

(3x^5-5)^7×15x^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)) .