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5.5_Logarithmic__Derivatives_with_space - • f(u =(3u-5...

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5.5 Derivatives of Natural Logarithmic Functions Derivative rule 1 for Natural Logarithmic Functions If y = ln x, then y ’= 1/x, x≠0. Derivative rule 2 for Natural Logarithmic Functions If y = ln f(x), where f(x) > 0 then y ’= f ’ (x)/ f (x) 1. Find the derivative of the function h(t) = 3 ln t 5 2. Find the derivative of the function f(x) = ln (5x 2 – 6x + 5) 3. Find the derivative of the function f(x) = ln (x 6 – 6) 2
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4. Find the derivative of the function f(x) = (ln u) 9 5. Find the derivative of the function f(x) = ln ((6x)/ (x+3)) 6. Find the derivative of the function f(u) = (3u-5) ln (5u
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Unformatted text preview: • f(u) = (3u-5) ln (5u 2 + 2) 7. Find the second derivative of the function • f(u) = ( ln u5 ) 2 • Note: f’(u) = 10 ln(u5 ) u 8. Natural logarithms have made it to the 21st century… • In a study conducted in 2004, the number of online households (in millions) in Western Europe was projected to be: • N (t) = 34.68 + 23.88 ln(1.05t + 5.3) [ 0, 2] where t = 0 corresponds to the beginning of 2004. How fast was this number growing at the beginning of last year? 9. Find the equation of the line tangent to the graph of f(x) = x ln(x 10 ) at x = 1...
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