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Answer 1 · 2017-10-15T12:03:33

See below.

We need to use the Quotient Rule to differentiate this. The quotient rule states if:

#y = u/v# then #dy/dx=( v (du)/dx-u (dv)/dx)/v^2#

#u =1#

#v=sqrt(t)#

#(du)/dt=0#

#(dv)/dt = 1/(2sqrt(t))#

#((sqrt(t)* 0- 1*1/(2sqrt(t))))/(t)=(-1/(2sqrt(t)))/t=-1/(2tsqrt(t)) =-1/(2t^(3/2))=-1/(2sqrt(t^3))#

Domain of #1/sqrt(t)#

#{t in RR: 0<=t<oo}#

Domain of # -1/(2t^(3/2)#

#2t^(3/2)= 2sqrt(t^3)#

For #RR#

#t^3 >=0#

Hence: #t >=0#

So domain is:

#{t in RR:0<=t<oo}#