Question

Which of the following expressions is the definition of the derivative of f(x) = ln(x) at the point (5, Ln(5))?

Answer 1

definition of the derivative is \[f'(x) = \lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h }\]

Your function is \(f(x) = \ln(x)\) so you need to first rewrite that definition replacing \(f\) with \(\ln\), then plug in the value of \(x\) at the specified point.

Answer 2

Thank you!!!

Answer 3

If you evaluate the limit in your answer with \(x=5\), you should get a value of \(f'(5) = 1/5\) if you did the work correctly, as the derivative of \(f(x) = \ln(x)\) is \(f'(x) = 1/x\).