Question

What is the derivative of a unit vector?

Answer 1

Hint : The derivative of any vector can be defined whether the vector is unit or not is simply the derivative of each component in the vector. Let us assume that some vector valued function $v(t)$ for example for which we divide its magnitude to get its unit vector. The derivative of the unit vector is simply the derivative of the vector.

Complete step-by-step answer :
Let us assume any vector first. To get the unit vector, first divide the vector with its magnitude.
To find the derivative of the unit vector, take the derivative of each component separately and this is performed for more than two dimensions.
Considering the unit vector to be just numbers then the derivative is zero because the derivative of any constant term is always zero.

The instantaneous rate of change of function at a point can be defined as the derivative of the function and it can be expressed as $f'(x) = \mathop {\lim }\limits_{h \to 0} \dfrac{{f(x + h) - f(x)}}{h}$ . One can find the instantaneous rate of change of the function at a point by finding the derivative of that function and placing it in the x-value of the point.
So, the correct answer is “0”.

Note : Instantaneous rate of change of the function can be represented by the slope of the line, which says how much the function is increasing or decreasing as the x-values change. It can also be defined as $\dfrac{{dy}}{{dx}}$
The instantaneous rate of change can be expressed as the change in the rate at a particular instant and it is the same as the change in the derivative value at a specific point.