(a)[1]
For $y = \ln(\ln x)$, show that $\frac{dy}{dx} = \frac{1}{x\ln x}$.
(b)[7]
The variables $x$ and $t$ are linked by the differential equation $x\ln x + t\frac{dx}{dt} = 0$. It is given that $x = e$ when $t = 2$. Solve the differential equation to find $x$ in terms of $t$, and simplify your result.
(c)[1]
Therefore state what happens to the value of $x$ as $t$ approaches infinity.