Question

Derivative of (sec^-1u)

Answer 1

The derivative of (sec^-1u) can be found using the chain rule and the derivative of the inverse of the secant function. The result is 1 / (u * sqrt(u^2 - 1)).

Step-by-step explanation:

The derivative of (sec^-1u) can be found using the chain rule of differentiation and the derivative of the inverse of the secant function.

1. Let y = sec^-1(u).
2. Then, sec(y) = u.
3. Take the derivative of both sides with respect to u:
4. sec(y) * tan(y) * dy/du = 1.
5. Substitute sec(y) with u:
6. u * tan(y) * dy/du = 1.
7. Solve for dy/du:
8. dy/du = 1 / (u * tan(y)).
9. Finally, substitute tan(y) with sqrt(u^2 - 1):
10. dy/du = 1 / (u * sqrt(u^2 - 1)).

Therefore, the derivative of (sec^-1u) is 1 / (u * sqrt(u^2 - 1)).