First of all, recall that y is a product of function of x. We have three factors:
[tex]f(x)=x^2,\quad g(x)=e^{3x},\quad h(x)=\sin(4x)[/tex]
The derivative of a product of function is computed by deriving one function at the time, and then adding all the results:
[tex]y' = f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)[/tex]
Let's compute the derivative of each function first:
[tex]f'(x)=2x,\quad g'(x) = 3e^{3x},\quad h'(x)=4\cos(4x)[/tex]
Now plug f, f', g, g', h, h' in the formula above as required:
[tex]2xe^{3x}\sin(4x)+3x^2e^{3x}\sin(4x)+4x^2e^{3x}\cos(4x)[/tex]
