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Solution - If y = f(x) is a differentiable function of x such that inverse function x = f^–1 (y) exists, then prove that x is a differentiable function of y and dx/dy=1/(dy/dx) where dy/dx≠0 - Derivative - Derivative of Inverse Function

Question

If y = f(x) is a differentiable function of x such that inverse function x = f–1 (y) exists, then prove that x is a differentiable function of y and `dx/dy=1/((dy/dx)) " where " dy/dx≠0`

 

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APPEARS IN

2012-2013 (October)
Question 5.1.2 | 3 marks
2015-2016 (July)
Question 5.1.3 | 2 marks
2016-2017 (March)
Question 5.2.1 | 4 marks
Solution for question: If y = f(x) is a differentiable function of x such that inverse function x = f^–1 (y) exists, then prove that x is a differentiable function of y and dx/dy=1/(dy/dx) where dy/dx≠0 concept: Derivative - Derivative of Inverse Function. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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