APFIVE Derivative of a Vector Valued Function
The vector-valued function $$\mathbf{r}$$ is defined by $$\mathbf{r}(t)= \langle e^{t}, \ln(t+1) \rangle$$ for $$t\ge0$$. What is $$\mathbf{r}'(t)$$?
A
The derivative is $$\langle e^{t},\frac{d}{dt}\ln(t+1) \rangle = \langle e^{t},\frac{1}{t} \rangle$$.
B
The derivative is $$\langle e^{t},\frac{1}{t+1} \rangle$$.
C
The derivative is $$\langle e^{t},\ln(t+1) \rangle$$.
D
The derivative is $$\langle e^{t},\frac{1}{\ln(t+1)} \rangle$$.
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