SECTION 5-1 The Derivative of the Natural Logarithm.

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Presentation transcript:

SECTION 5-1 The Derivative of the Natural Logarithm

Natural Logarithm Natural logarithm Logarithm with base e, where e ≈ ln(e) = 1

Properties of the Natural Logarithm 1) Domain (0, ∞ ) and Range (-∞, ∞) 2) The function is continuous, increasing, and one to one 3) The graph is concave down

1.) Use the properties to rewrite the expression

Let u be a differentiable function of x such that general Chain rule absolute value Derivative of the natural logarithm

Find the derivative

Assignment Page 331 # 7-10, 31, 32, 34, all, 57, 61, 63, 69, and 71