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Differentiation of the Exponential Function (e x ) and Natural Logarithms (lnx) Exponential function e x

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Exponential function of the type

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Natural Logarithm function lnx

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Exponential function of the type

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Determine the nature of any stationary points on the curve Differentiate Any thing raised to the power of zero is 1 or ln(1) = 0 When x = ½, y = e 0 - 1 = 0 Stationary point at ( ½, 0) > 0 Minimum point Therefore ( ½, 0 ) is a minimum point.

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Determine the nature of any stationary points on the curve Differentiate When x = 1, y = 1 - 0 = 1 Stationary point at ( 1, 1) > 0 Minimum point Therefore (1, 1) is a minimum point. Sketch

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Determine the nature of any stationary points on the curve Differentiate When x = 1, y = 1 - 0 = 1 Stationary point at ( 1, 1) > 0 Minimum point Therefore (1, 1) is a minimum point. Sketch

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NATURAL LOGARITHMS. The Constant: e e is a constant very similar to π. Π = 3.141592654… e = 2.718281828… Because it is a fixed number we can find e 2.

NATURAL LOGARITHMS. The Constant: e e is a constant very similar to π. Π = 3.141592654… e = 2.718281828… Because it is a fixed number we can find e 2.

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