f(t)=lim t*[(x+t)/(x-t)]^x
=lim t*[1+2t/(x-t)]^[(x-t)/2t*2tx/(x-t)]
=lim t*e^[2tx/(x-t)]
=t*e^(2t)
f'(t)=e^(2t)+2te^(2t)
=(2t+1)e^(2t)
f(t)=lim t*[(x+t)/(x-t)]^x
=lim t*[1+2t/(x-t)]^[(x-t)/2t*2tx/(x-t)]
=lim t*e^[2tx/(x-t)]
=t*e^(2t)
f'(t)=e^(2t)+2te^(2t)
=(2t+1)e^(2t)