2025 RI Techniques of Differentiation Assignment 6A Q3

2025 RI Techniques of Differentiation Assignment 6A Q3

5 marks
Tutorial

Given that a curve has the equation \({{x}^{{{\tan }^{-1}}x}}={{y}^{x+1}}\) where \(x>0\) and \(y>0\), using a non-calculator method, find the exact gradient of the curve at the point where \(x=1\).[5]

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Answer:\(\dfrac{\pi}{8}\)

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