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

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