Shortcut rules for derivatives
Notice these rules all use the same notation for derivative. The image at the top of this page displays several ways to notate higher-order derivatives. Each notation has advantages in different situations. See below for a summary of the ways to notate first derivatives.
Be careful applying these rules. The "u" and "v" represents functions; "c" and "n" only represent constants.
Notation
This notation illustrates taking the derivative of y with respect to x. It is read "D y D x". It is probably the most widely used notation and allows the mathematician to illustrate both what is being differentiated and with respect to which variable. It also indicates that it is similar to the familiar slope calculation "change in y over change in x."
Similar to the notation above, this notation allows you to demonstrate both what is being differentiated and with respect to which variable. This simply allows the mathematician to use an expression in the parentheses instead of another defined equation y. It is read "D D x".
This notation is very short and quick. It is pronounced "D x".
Pronounced "y prime", this notation is the shortest and possibly the second most widely used because of its convenience. However, its disadvantage is that it does not give the information of differentiation with respect to what variable.
Ready for practice?
This website gives random derivative problems for you to try and tells you whether your answer is correct or incorrect. You can adjust the level of difficulty. However, you do need to be somewhat familiar with computer syntax (for example: use "^" to raise something to an exponent and "/" for division, and when in doubt, use parentheses.)
Derivative Practice Website
This website provides an online multiple choice quiz over differentiation rules.
Visual Calculus
Derivative Practice Website
This website provides an online multiple choice quiz over differentiation rules.
Visual Calculus
Here is a worksheet of extra practice problems for differentiation rules. These are mostly challenging problems; I recommend you do the book assignments for Chapter 2 first. For a list of book assignments, visit the Homework Assignments section of this website.
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