Key to "Derivatives of vector-valued functions Differentiate the following function...." - Plainmath

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dailinoyf

Answered question

2021-11-27

Derivatives of vector-valued functions Differentiate the following function.
$r (t) = ⟨ 2 t^{3}, 6 \sqrt{t}, \frac{3}{t} ⟩$

Answer & Explanation

Vincent Diaz

Beginner2021-11-28Added 19 answers

Step 1
We have given the function;

r (t) = ⟨ 2 t^{3}, 6 \sqrt{t}, \frac{3}{t} ⟩

Step 2
We differentiate the function by using

\frac{d}{d x} x^{n} = n x^{n - 1}

he derivative of the function with respect to t will be;

r ‘ (t) = ⟨ \frac{d}{d x} 2 t^{3}, \frac{d}{d x} 6 \sqrt{t}, \frac{d}{d x} \frac{3}{t} ⟩

r ‘ (t) = ⟨ 6 t^{2}, 6 \frac{1}{2} \frac{1}{\sqrt{t}}, - \frac{3}{t^{2}} ⟩

r ‘ (t) = ⟨ 6 t^{2}, 3 \frac{1}{\sqrt{t}}, - \frac{3}{t^{2}} ⟩

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