About differentiation~~~

The 1st derivative of 2( x^2 ) sinx ( cosx )^3

= 2( 2x ) sinx ( cosx )^3
+ 2( x^2 )( cosx )( cosx )^3
+ 2( x^2 ) sinx [ 3( cosx )^2 ( -sinx ) ]

= 2x sinx ( cosx )^2 [ 4 cosx + x( cosx )^2 - 3x( sinx )^2 ]
= 2x sinx ( cosx )^2 [ 4 cosx + x( cosx )^2 - 3x + 3x( cosx )^2 ]
= 2x sinx ( cosx )^2 [ 4 cosx + 4x( cosx )^2 - 3x ]

Actually you need to use Chain Rule and Product Rule together in solving this problem.

Is theta independent to x?

variable is x or θ ?

with respect to which variable?
to x, or to the angle?