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Unformatted text preview: 11.2 The derivative of the inverse functions Consider the inverse function y = arcsin( x ). We can determine the derivative of this function by invoking the Chain rule. We proceed as follows: 11.2.1 All derivatives of the inverse trig functions are determined in this way : We prove that Proof : 11.3 Example For the given function f ( x ) find f ( x ). 11.4 Derivatives of inverse hyperbolic functions. Solution: 11.5 A general expression for the derivative of f 1 ( x ). If y = f 1 ( x ) then Proof: 11.5.1 Example We find the derivative of tanh 1 ( x ). Recall from lecture 3 that tanh 1 ( x ) is only defined for  x  < 1. Also from lecture 3 recall the identity sech 2 x = 1 tanh 2 x . Given: where  x  < 1. 11.5.2 Exercise By mimicking the proof in example 11.4 show that the derivative of cosh 1 ( x ) is Derivatives of logarithmic functions log a x will be discussed in the next lecture....
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.
 Spring '11
 RobertAndre
 Calculus, Derivative

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