remember the chain rule
dy/dx f(x)g(x)=f'(x)g(x)+g'(x)f(x)dd
and dy/dx cos(x)=-sin(x)
and dy/dx sin(x)=cos(x)
so
[tex]\frac{dy}{dx} x^2cos(x)=2xcos(x)+(-x^2sin(x))=2xcos(x)-x^2sin(x)[/tex]
2nd derivitive
[tex]\frac{dy}{dx}2xcos(x)-x^2sin(x)=2cos(x)+(-2xsin(x))-(2xsin(x)+x^2cos(x))=2cos(x)-2xsin(x)-2xsin(x)-x^2cos(x)=[/tex]
[tex]2cos(x)-x^2cos(x)-4xsin(x)[/tex]
true
