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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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 Spring '11
 RobertAndre
 Calculus, Derivative, Inverse function, Logarithm, Inverse trigonometric functions, Hyperbolic function, inverse trig functions

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