Question

Найти f′′(x) , если f(x)=sin2x3

Answer 1

$f(x)=sin(2x^3)\f'(x)=cos(2x^3)*(2x^3)'=cos(2x^3)*(6x^2)\f''(x)=(cos(2x^3))'*(6x^2)+(6x^2)'*(cos(2x^3))=-(sin(2x^3))*((2x^3))'*(6x^2)+12x*(cos(2x^3))=-36x^4*sin(2x^3)+12x*cos(2x^3)$

Answer 2

$f(x)=sin^23x\\f'(x)=2sin, 3xcdot cos, 3xcdot 3=3cdot sin, 6x\\f''(x)=3cdot cos, 6xcdot 6=18cdot cos, 6x\\f'''(x)=18cdot (-sin, 6x)cdot 6=-108cdot sin, 6x$