Solved: Derivatives of vector-valued functions

Chapter 11, Problem 7E

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QUESTION:

7-12. Derivatives of vector-valued functions Differentiate the following functions.

\(\mathbf{r}(t)=\left\langle 2 t^{3}, 6 \sqrt{t}, 3 / t\right\rangle\)

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QUESTION:

7-12. Derivatives of vector-valued functions Differentiate the following functions.

\(\mathbf{r}(t)=\left\langle 2 t^{3}, 6 \sqrt{t}, 3 / t\right\rangle\)

ANSWER:

Solution 7EStep 1:In this problem we need to differentiate the following functions, Let , where f, g, and h are differentiable functions on . Then r has a derivative (or is differentiable) on and .

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