Find the slope of the tangent line to the function y = In x at the point x = 2.

Solution:

Given, the function is y = ln x

The point is x = 2.

We have to find the slope of the tangent line to the function.

At x = 2,

y = ln(2)

y = 0.6931

Therefore, the point on the curve is (2, 0.69)

On differentiating,

dy/dx = 1/x

At x = 2

dy/dx = 1/2

Therefore, the slope of the tangent line is 1/2.

Find the slope of the tangent line to the function y = In x at the point x = 2.

Summary:

The slope of the tangent line to the function y = ln at the point x = 2 is 1/2.