Calculus Help Please?
Please, I DO NOT WANT TO KNOW HOW TO FIND THE DERIVATIVE OF THIS.. I ALREADY KNOW HOW.. The answer to this should be a value.. but I'm not sure how to approach it.
Can you help me solve this math question?
f(x) = 2X + (cos x)^2
What is: Derivative of(Inverse of f) at the value 1?
Please explain how you got the answer.
- DukeLv 61 decade agoFavorite Answer
You use the Thm that if g is the inverse of f, then
g '(a) = 1/[ f '( g(a) ) ].
In this problem we need to find g '(1).
To use the above formula, we first need to get g(1).
g(1) must equal 0, because f(0) = 2*0 + (cos 0)^2 = 1.
Then we need f '( g(a) ) which will be f '(0)
Now f '(x) = 2 - 2cos(x)sin(x) , so f'(0)= 2.
Plugging into the formula: g '(1) = 1/2.