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The power rule can be proved using implicit differentiation for the case where n is a rational number , and is assumed beforehand to be a differentiable function . If then . Use Implicit differentiation to show that

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Deanna Hettinger
Deanna HettingerLv2
14 May 2020

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15] 2: (a) Approximate the value of 5 by finding the approximations by and Method is applied to the function () == -5 starting with = 1. when Newton's 15] (b) Let y = y(a) be defined implicitly by the equation y + xy = + 3y with 9(2) = 1. Use implicit differentiation to find y'(2), then use the linearization of g() at = 2 to approximate the value of 9).

Use the chain Rule to show that if is measured in degrees, then

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3. (20 pts) Let f be a differentiable one-to-one function on the interval (0,4) with the particular values of f and f' given in the table below, and let f-1 be the inverse function of f. Let g be the function given by the graph below. y y=g(x) 12 2 3 5 1 2 3 4 5 6 34-2 For (a), (b), and (c), circle the correct choice. lim 8(3+h) – g(3) h iii. 5 V. -2 vi. does not exist vii. none of the previous choices iv. O (b) dip [6^x +2)/(x) at x = 3 iii. 1 V. -1 vii. none of the previous choices iv. 0 vi. does not exist (0) [r_w) at x = 2 V. vii. none of the previous choices iv. I vi. does not exist (d) Consider the curve given by xey + y = f(x) - 1. Use implicit differentiation to computed at the point (2.0). Show your work.

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