`f(x) = ln(x^2 - 2x)` Differentiate f and find the domain of f.

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Chapter 3, 3.6 - Problem 29 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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embizze | High School Teacher | (Level 1) Educator Emeritus

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Differentiate `f(x)=ln(x^2-2x) ` and find the domain of f:

The domain is all possible inputs. The natural logarithm is defined for all inputs greater than 0, so `x^2-2x>0 ==> x<0,x>2 ` .

The derivative of `ln(u) ` is `(u')/u ` where u is a differentiable function of x.

`f'(x)=(2x-2)/(x^2-2x) `

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