Question: This exercise shows another way to derive the formula for the derivative of the natural logarithm function using the definition of the derivative. (a) Using

This exercise shows another way to derive the formula for the derivative of the natural logarithm function using the definition of the derivative.

(a) Using the definition of the derivative, show thatd(In x) dx = lim In 1 + h0 h1/h X

(b) Eliminate h from the result in part (a) using the substitution h = x/m to show that

(c) What property should the function g have that would yield

(d) Assuming that the natural logarithm has the property in part (c), and using a result about

d(In x) dx = lim In 1 + h0 h1/h X

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