Question

How to differentiate sin(arcsec(x))

Answer 1

To differentiate sin(arcsec(x)), use the chain rule. Find the derivative of arcsec(x), differentiate sin(u) with respect to u, then multiply both derivatives.

Step-by-step explanation:

To differentiate sin(arcsec(x)), we can use the chain rule. Let's start by finding the derivative of arcsec(x).

Using the chain rule, we have:

1. Let u = arcsec(x).
2. Find the derivative of u with respect to x.
3. Using the fact that d(arcsec(x))/dx = 1/(|x|sqrt(x^2-1)), we can substitute the derivative of u back into the original expression.
4. Now differentiate sin(u) with respect to u to get cos(u).
5. Finally, multiply the derivative of u by the derivative of sin(u) to get the final result.

Therefore, the derivative of sin(arcsec(x)) is cos(arcsec(x))/(|x|sqrt(x^2-1)).