On my Calc II quiz today, I couldn't figure out how to do this one problem, and it's driving me nuts just thinking about it... How would you solve it?
f(x)=x^3+3sin(x)+2cos(x)
a=2
Find f-1'(a)
Note that that is the derivative of the inverse function of f. This problem would be easy if I could solve for f-1 and plug it into f-1'(x)=1/(f'(f-1(x)), but I couldn't see any way to do that. I racked my brain thinking of a way to implicitly solve for it, but I came up with a blank. Any help?