Question

Is the following true or false?

the second derivative of the quantity x squared times the cosine of x equals 2 times cosine x minus 4 times x times sine of x minus x squared times cosine x

See attached for the problem

Answer 1

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

`(dy)/(dx) x^2cos(x)=2xcos(x)+(-x^2sin(x))=2xcos(x)-x^2sin(x)`
2nd derivitive

`(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)=`

`2cos(x)-x^2cos(x)-4xsin(x)`
true

Answer 2

the following answer would be
true