`f(u) = u/(1 + ln(u))` Differentiate the function.

Textbook Question

Chapter 3, 3.6 - Problem 10 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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`f(u) = u/{1 + lnu}`

`f'(u) = {(1+lnu)*((du)/(du)) - u*[d(1+lnu)/(du)]}/(1+lnu)^2`

`or, f'(u) = [(1+lnu) - (u/u)]/(1+lnu)^2`

`or, f'(u) = (1 + lnu - 1)/(1+lnu)^2`

`or, f'(u) = lnu/(1+lnu)^2`

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