1 The slopes of the tangent line are parallel to each other where the original and inverse of the function are shown Consequently the values of x and y are flipped around which shows a transformation of both functions 2 The chain rule is related to the derivative of inverse functions because when differentiating f f 1 x the answer is 1 f f 1 x As this is the rule for an inverse function when you flip the values accordingly 3 When using the inverse function theorem you can extend the power rule by using differentiation concerning a given quantity Where you apply the chain rule to the inverse function to attain the derivative 4 The derivative of lnx is equal to 1 x because when given values ln x y where e y x Differentiating both sides of the equation the derivative ends up being 1 x About its regular inverse function a lot can be proved with the inverse function theorem in calculus such as finding the inverse derivative of trig functions A N A B N A C I spent 45 min on this assignment I pledge my honor that I have abided to the Stevens Honor System