the question is....Let f(x)=x^3+x. If h is the inverse function of f, then h'(2)=
the answer is 1/4, but I dont understand how to do it..this problem is from the collegeboard clep guide and it doesn't explain any problems.
Thanks for any help I can get
no, that is NOT what you should do. that is finding notthis is what I have been doing.
1/(x^3+x)...I start with that, then I take the derivative of that
even if you were correct to do this, this is still wrong. this is not how you find the derivative of a fractionx^-3+x^-1
= 1/ (-3x^4-x^2)
ok, let's take this slow.
the formula is:
we want , it means we must find and plug it into (this, of course, means we also have to find )to get and then plug it into the formula.
first we find :
ok, that wasn't so hard.
now let's find . since , this amounts to finding an such that
thus we must solve:
it is almost obvious that
this means that .
now we just plug that into our formula: