Is the graph of y=sin (x^6) increasing or decreasing when x=12

The rate of change, i. e. slope of

y=sin (x^6)

is

y'=dy/dx=cos (x^6) * (6x^5)

Substitute x=12 (radians)

y' (12) = cos (12^6) * (6*12^5)

=1492992cos (2985984)

=1128592.5 >0

Therefore y (x) is increasing at x=12 (radians).