Find all values of x where the tangent line is horizontal for the function f (x) = x/x^2+5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Find all values of x where the tangent line is horizontal for the function f (x) = x/x^2+5

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Follow-up Question

why is it f'(x)=(x^2+5)(1)-x(2x)/(x^2+5)^2 

where did the (1) and 2x come from in the numerator? please explain

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