Question

If $x=t$ log $t$ and $y=t^t$ then find $\frac{dy}{dx}$

Answer 1

$\begin{array}{c}x=t\log t\\ y=t^t\\ \frac{dy}{dt}=t^t\left(1+\log t\right)\\ \frac{dx}{dt}=1+\log t\\ \frac{dy}{dx}=\frac{dy/dt}{dx/dt}\\ \therefore \frac{dy}{dt}=t^t\end{array}$

Hence, this is the answer.