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Natural logarithm derivatives

Natural logarithm derivatives

7 marks
TGM Original
Given y=- ln(x) + ln(x2 + 1), x>0, find dydx. Find all zero-gradient inputs in the stated domain.

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Answer:\(\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{2 x}{x^{2} + 1} - \dfrac{1}{x}\) The only zero-gradient input is \(x=1\).

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