Verified Answer :

\(f(t)=2t^3+t\\\\f'(t)=3\cdot2t^{3-1}+1=6t^2+1\\\\\boxed{f'(a)=6a^2+1}\)

using derivations laws 
f(t) = 2t^3 + t
f'(t)=6t^2+1
substituting a instead of t
f'(a)=6a^2+1
hope it helps