Higher Derivatives

 

We said before the first derivative of a function f(x) is also a function in x. Therefore, it may be differentiated again with respect to x. Then we get the second derivative (or the derivative of the second order) of x, which is also a function of x. In the same way, we can differentiate the second derivative to get the third derivative then the fourth derivative…etc. Here are some ways to symbolize higher derivatives.

 

 

First derivative

Second derivative

Third derivative

Fourth derivative

nth derivative

Example

Given that , Find .

 

Solution

Example

Given that , find .

 

Solution