What is the slope of the line tangent to the graph of y = ln(2x) at the point where x = 4

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

Given:

Equation is y = ln(2x)

We have to find the slope of the line tangent to the graph y = ln(2)

Differentiating the given equation y = ln(2x),

⇒ dy/dx = d(ln(2x))/dx

⇒ dy/dx = 2/2x

⇒ dy/dx = 1/x

Slope, dy/dx at x = 4 is given by 1/x = 1/4.

Therefore, the slope of the tangent line is 1/4.

What is the slope of the line tangent to the graph of y = ln(2x) at the point where x = 4

Summary:

The slope of the line tangent to the graph of y = ln(2x) at the point where x = 4 is 1/4.