To find the slope of the tangent line to the graph of y = ln(2x) at the point where x = 4, we need to differentiate the function and then evaluate the derivative at that particular value of x.
Step 1: Differentiate the function
First, let’s differentiate y = ln(2x). Using the chain rule, the derivative of ln(u) where u = 2x is given by:
dy/dx = (1/u) * (du/dx)
Now substituting for u: u = 2x, thus du/dx = 2. Now we apply this:
dy/dx = (1/(2x)) * 2 = 1/x
Step 2: Evaluate the derivative at x = 4
Now we evaluate the derivative at x = 4:
dy/dx = 1/4
Conclusion
Thus, the slope of the tangent line to the graph of y = ln(2x) at the point where x = 4 is 1/4.