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

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Presentation transcript:

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

Exponential function of the type

Natural Logarithm function lnx

Exponential function of the type

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  Stationary point at ( ½, 0) > 0  Minimum point Therefore ( ½, 0 ) is a minimum point.

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

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