Question

Производные найти функцию

Answer 1

Ответ:

y = 1

y ` = (1) ` = 0

y = x

y` = (x) ` = 1

y = 2x

y ` = (2x) ` = 2

y = x^2

y ` = (x^2) ` = 2x

y = 3x^3 + 3

y ` = (3x^3 + 3) ` = 9x^2 + 0 = 9x^2

y = 4x^4 + 1/3 x^3 + 1/2 x^2 + 4

y ` = (4x^4 + 1/3 x^3 + 1/2 x^2 + 4) ` = 16x^3 + x^2 + x

y = (2x^3 - 3)(3x^2 - 2) = 6x^5 - 4x^3 - 9x^2 + 6

y ` = (6x^5 - 4x^3 - 9x^2 + 6) ` = 30x^4 - 12x^2 - 18x

y = (5x^2) / (x+1)

y ` = ( (5x^2) ` × (x+1) - (5x^2) × (x+1) ` ) / ( (x+1)^2 ) = ( 10x × (x+1) - (5x^2) × 1 ) / ( (x+1)^2 ) = (10x^2 + 10x - 5x^2) / ( (x+1)^2 ) = ( 5x^2 + 10x ) / ( (x+1)^2 )

СПРАВОЧНИК:

(C) ` = 0

(x) ` = 1

(x^n) ` = nx^n-1

(u + v) ` = (u) ` + (v) `

(u/v) ` = ( (u)` × (v) - (u) × (v) ` ) / v^2