Question

Производная 10 класс 4 вариант

Answer 1

$1) (x^4+5)' = (x^4)' + 5' = 4x^3$
$2)(7x-1/x)' = (7x)' - (x^-1)' = 7 + 1/x^2$
$3)( sqrt{x} +3x^3)'= (sqrt{x})' + (3x^3)' = 1/(2sqrt{x}) +9x^2$
$4)(1/5x^3+3 sqrt{x} +4/x)' = 0,6x^2 + 3/(2 sqrt{x} ) + 4/x^2$
$5)((4x-6)(3x^5+2x- sqrt{5}))' = \ (4x-6)'(3x^5-2x+sqrt{5})+ (4x-6)(3x^5-2x+sqrt{5})' = \ 12x^5-8x+4 sqrt{5} +(4x-6)(15x^4+2) = \ 2(-36x^5+45x^4-8x+2 sqrt{5} +6)$
$6)((x^3+5x)/(x^2-4x))' = \ ((x^3+5x)'(x^2-4x)-(x^3+5x)(x^2-4x)')/(x^2-4x)^2 = \ (3x^4-7x^2-20 -2x^4+4x^3-10x^2+20)/(x^4-8x^3+16x^2) = \ (x^2-8x-5)/(x-4)^2$