Differentiation - logarithmic functions

The relationship between the graphs of the exponential function and the logarithmic function is demonstrated by this Exploremath activity. (The slider can be moved to show a = e.)

y = ln x  is the inverse function of  y = e^x .

Each graph is the reflection of the other in the line y = x.

Consider the point on the graph of  y = e^x  where y = 2. The gradient of the tangent is 2.

The reflection of this point lies on the graph of  y = ln x  where x = 2. The gradient of the tangent is ½.

Consider the application of the chain rule to logarithmic functions.

In the result, the numerator is the derivative of the denominator.

To differentiate logarithmic functions more easily, use the properties of logarithms.