Page 25 of the Formulae and Tables booklet gives a table with some standard functions of x and their derivatives as shown below left. Below right I have added a version that shows how these can be applied to functions of functions of x. In these cases we need to use the chain rule. In the blank box in entries on the table on the right the inner function is placed. The shaded box represents the derivative of what is placed in the blank box. Some students might find this more visual representation of the chain rule useful.

For example to get the derivative of cos(3x+5), the outer function is cos ( ) which has as derivative -sin( ). The inner function is (3x+5) which has derivative 3. Using the chain rule the derivative of cos(3x+5) is -3sin(3x+5).

You will find this and lots more in the downloadable PDF file “Making the most of the Formulae and Tables Booklet” which can be purchased at https://sellfy.com/p/qR3F/

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