What is the derivative of (u•v)
(u’•v)+(u•v’)
The derivative of (u・v), where u and v are vectors, depends on whether we are taking the dot product or the cross product.
If we are taking the dot product, the formula for the derivative is:
d/dt (u・v) = (du/dt)・v + u・(dv/dt)
Here, the dot (・) represents the dot product, and du/dt and dv/dt represent the derivatives of vectors u and v, respectively, with respect to time t.
We can see that the derivative of the dot product is a vector itself, and it consists of two components: (i) the derivative of u with respect to time multiplied by vector v, and (ii) vector u multiplied by the derivative of v with respect to time.
On the other hand, if we are taking the cross product, then there is no derivative of (u・v), since the cross product is not a differentiable operation.
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