What is the slope of the line tangent to the graph of y = ln(1 + x) at x = 1?

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The slope of the line tangent to the graph of a function at a given point is determined by the derivative of that function evaluated at that point. In this case, we want to find the slope of the tangent line to the graph of y = ln(1 + x) at x = 1.

To perform this calculation, we will go through the following steps:

  1. Find the derivative: We start by taking the derivative of the function y = ln(1 + x). Using the chain rule, the derivative is given by:

    2. y’ = 1/(1 + x)

  2. Evaluate the derivative at x = 1: Now, we substitute x = 1 into the derivative we found:

    3. y'(1) = 1/(1 + 1) = 1/2

  3. Interpret the result: Thus, the slope of the tangent line to the graph of y = ln(1 + x) at the point where x = 1 is 1/2.

In summary, the slope of the tangent line to the graph of y = ln(1 + x) at x = 1 is 1/2.

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