Answer:
1/4
Explanation:
The slope of the line tangent to a function at a certain point is the derivative of that function evaluated at that point. This is because a derivative is an instantaneous rate of change, and when evaluated at a point, it gives a slope at a specific point, hence the tangent line. (This is easier to visualize if you draw it)
So, to find the derivative of ln(2x), you need to apply the chain rule. The chain rule says that to find the derivative of a composite function (Let's call it f(g(x)), where the input of f is equal to the output of g using the input x), is equal to f'(g((x)) · g'(x). In this case, ln(x) is f(x), and 2x is g(x). The derivative of㏑(x) is 1/x, so f'(g(x)) is 1/(2x). Multiply by g'(x), you get (1/2x)·2x, which is equal to 1/x. So, the derivative of ln(2x) is 1/x.
Now, we need to evaluate it at x = 4. Simply plug this value into 1/x to get 1/4.