Find out the answer to "Compute the derivative of the vector-valued function r(t)=⟨sin⁡2t,"

Virginia Caron

Answered question

2021-11-30

Compute the derivative of the vector-valued function

r (t) = ⟨ \sin 2 t, e^{t^{2}} ⟩

Margaret Plemons

Beginner2021-12-01Added 13 answers

Step 1
If

r (t) = ⟨ f (t), g (t), h (t) ⟩

where f, g, h are differentiable function, then

r^{'} (t) = ⟨ f^{'} (t), g^{'} (t), h^{'} (t) ⟩

Step 2
Given,

r (t) = ⟨ \sin 2 t, e^{t^{2}} ⟩

\frac{d}{d t} (\sin 2 t) = \cos 2 t \frac{d}{d t} (2 t)

= 2 \cos 2 t

\frac{d}{d t} (e^{t^{2}}) = e^{t^{2}} \frac{d}{d t} (t^{2})

= 2 t e^{t^{2}}

So,

r^{'} (t) = ⟨ 2 \cos 2 t, 2 t e^{t^{2}} ⟩

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?