To find the slope of the line tangent to the curve y = ln(1 + x) at the point where x = 1, we first need to determine the derivative of the function.
The derivative of y = ln(1 + x) with respect to x can be calculated using the chain rule. The derivative is:
y’ = (1 / (1 + x)) * (d/dx(1 + x))
Since the derivative of 1 + x is simply 1, we have:
y’ = 1 / (1 + x)
Next, we substitute x = 1 into the derivative to find the slope of the tangent line at this specific point:
y'(1) = 1 / (1 + 1) = 1 / 2
Therefore, the slope of the line tangent to the graph of y = ln(1 + x) at x = 1 is 1/2.