# How to find instantaneous rate of change for #f(x) = ln(x)# at x=5?

graph{ y-lnx)=0 [-0.365, 17.415, -3.44, 5.45]}/(y-ln(5)-1/5(x-5))

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To find the instantaneous rate of change for ( f(x) = \ln(x) ) at ( x = 5 ), we can use the derivative of the natural logarithm function. The derivative of ( \ln(x) ) with respect to ( x ) is ( \frac{1}{x} ). Therefore, the instantaneous rate of change of ( f(x) ) at ( x = 5 ) is equal to ( \frac{1}{5} ), or 0.2.

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