General Derivative of the Inverse of a Function: In this problem you will derive a
Chapter 4, Problem 29(choose chapter or problem)
General Derivative of the Inverse of a Function: In this problem you will derive a general formula for the derivative of the inverse of a function. a. Let y = sin1 x. Show that . b. By directly substituting sin1 x for y in part a, you get . Show that this equation and the derivative of sin1 x given in this section give the same value when x = 0.6. c. Show that this property is true for the derivative of the inverse of a function: d. Suppose that f(x) = x3 + x. Let h be the inverse function of f. Find x if f(x) = 10. Use the result and the property given above to calculate (10)
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