Question

Find the derivative of r(t) = arcsin(t), arccos(t), 0

Answer 1

The derivative of r(t) = arcsin(t), arccos(t), 0 is r'(t) = 1/sqrt(1-t^2), -1/sqrt(1-t^2), 0.

Step-by-step explanation:

The derivative of r(t) = arcsin(t), arccos(t), 0 can be found using the chain rule. Let's find the derivative of each term separately:

1. Derivative of arcsin(t): The derivative of arcsin(t) is 1/sqrt(1-t^2).
2. Derivative of arccos(t): The derivative of arccos(t) is -1/sqrt(1-t^2).
3. Derivative of 0: The derivative of a constant is zero.

Therefore, the derivative of r(t) = arcsin(t), arccos(t), 0 is r'(t) = 1/sqrt(1-t^2), -1/sqrt(1-t^2), 0.