Answer
Result See proof
Work Step by Step
Step 1 Let \[ r(t) = x(t)i + y(t)j \] Then \[ r(\tau(t)) = x(\tau(t))i + y(\tau(t))j \] Hence \[ \frac{d}{dt}r(\tau(t)) = \frac{d}{d\tau}x(\tau(t))i + \frac{d}{d\tau}y(\tau(t))j = x'(\tau(t))\frac{dt}{d\tau}i + y'(\tau(t))\frac{dt}{d\tau}j = \frac{dt}{d\tau}\frac{d\mathbf{r}(\tau(t))}{d\tau} \]
