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Students will use the Chain Rule to find the derivative of more complex exponential and logarithmic functions.
Students begin the activity by using the graph of the natural logarithm to estimate the graph of its derivative function. They will inspect the slope of a tangent to the graph of the natural logarithm function and create a scatter plot that models this information. Students will find a function that fits the scatter plot.
Next, students will generalize their findings for any logarithmic function.
Finally, students will investigate an interesting property related to a tangent to y = ln x.
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