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.

1 Answer

  • Duke
    Lv 6
    1 decade ago
    Favorite 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.

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