Finding an inverse combined trigonometric derivative

[severe sable]

I’m self studying for Calc II over this summer to hopefully place out of it come next month. I’ve been using some past handouts to accomplish this, but have run into a particularly tricky problem that I’m not sure how to approach.

Any advice would be appreciated. Struggling to see how to find the inverse function here, as I don’t see how to isolate for x.

[trail tree]

So here's a thing. Are you familiar with the general derivative of an inverse function?

[severe sable]

Nope, just looked it up though and looks like it should do the trick 😁, thanks for the tip

[wispy perch]

@severe sable has given 1 rep to @trail tree

[trail tree]

No problem.