Question
A vector function $\mathbf{r}(t)$ and scalar function $t=f(\tau)$ are given. Find $\frac{d \mathbf{r}}{d \tau}$.$$\mathbf{r}(t)=\left\langle\sec t, 1 / t, e^{t} \ln t\right\rangle, t=\tau^{-1}$$
Step 1
$$\frac{d \mathbf{r}}{d t} = \left\langle \frac{d}{dt}(\sec t), \frac{d}{dt}(1/t), \frac{d}{dt}(e^{t} \ln t) \right\rangle$$ $$\frac{d \mathbf{r}}{d t} = \left\langle \sec t \tan t, -\frac{1}{t^2}, e^{t} \ln t + e^{t}/t \right\rangle$$ Show more…
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