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Derivative of Natural Log Function

Displayed below is a graph of the function . Drag the BIG WHITE POINT along the graph of this function to trace out the graph of the derivative of this function. Does this function look familiar? Interact with this applet for a minute, then answer the question that follows.


Why is the derivative of the function never negative? Explain how you know.


Rewrite the equation in exponential form.


Use implicit differentiation to differentiate both sides of this equation (you wrote in your response for (2)) with respect to x. Then solve for y. What do you get?


Rewrite solely in terms of x.