How do you graph the derivative of #f(x) = log (x)#?

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Answer 1 · 2017-12-22T22:14:21

See below.

First we need to find the derivative of #f(x)=log(x)#

#d/dx(log(x))=1/x#

as #x->0^-color(white)(88888)# ,#1/x->-oo#

as #x->0^+color(white)(888)# , #1/x->oo#

The y axis is a vertical asymptote.

as #x->oocolor(white)(88888)# ,#1/x->0#

as #x->-oocolor(white)(888)# ,#1/x->0#

The x axis is a horizontal asymptote.

GRAPH:

graph{y=1/x [-16.02, 16.01, -8.01, 8.01]}