#### Answer

$u'=-\dfrac{2}{t^3}+\dfrac{1}{\sqrt{t^3}}+1$

#### Work Step by Step

Simplify the expression
$u=(t^{-1}-t^{-1/2})^2$
Apply newton's binomial formula: $(a-b)^2=a^2-2ab+b^2$
$u=(t^{-1})^2-2(t^{-1})(t^{-1/2})+(t^{-1/2})^2$
$u=t^{-2}-2t^{-3/2}+t$
Apply power rule to derivate
$u'=(-2)t^{-2-1}-2(\dfrac{1}{2})t^{-1/2-1}+(1)t^{1-1}$
$u'=-\dfrac{2}{t^3}+\dfrac{1}{\sqrt{t^3}}+1$