How do you find the instantaneous rate of change of the function # f(x)= ln (2x)# when x=3?

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Answer 1 · 2016-04-08T20:01:08

#1/3#

Instantaneous rate of change just means the derivative or gradient at a point.

To differentiate the function, we do

#f(x) = ln2x = ln2 + lnx#

and, because #ln2# is just a constant and has a derivative of #0#,

#f(x) = lnx#
#f'(x) = 1/x#

Now, when #x = 3#,

#1/x = 1/3#