Given ( w = f(s³t²) ) and ( f'(x) = eˣ ), find ( ∂ w/∂ t ) and ( ∂² w/∂ s² ).
a) ( 6s²t ) and ( 6t² )
b) ( 6s² ) and ( 6t )
c) ( 9s²t ) and ( 4t² )
d) ( 9s² ) and ( 4t )