What is the derivative of ##ln(1+(1/x))##?
February 20th, 2023
##d/dx(ln(1+(1/x))) = (-1)/(x(x+1))##
Although you could use ##d/dx (ln(u)) = 1/u (du)/dx##, the algebra will get messy that way.
Let’s rewrite using properties of ##ln##.
##y = ln(1+(1/x)) = ln((x+1)/x)##
## = ln(x+1) – ln(x)##
So
##dy/dx = 1/(x+1) – 1/x = (-1)/(x(x+1))##
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