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## Differentiation

Maple knows all the rules of differentiation and can differentiate any expression, no matter how complex it is. Using Maple to check your work (or do your work!) in problem sets where calculus is required is a major purpose of Maple. Differentiation can be done using several different approaches.

Enter the `diff(expr, x)` command and the expression `expr` will be differentiated with respect to the variable `x` or whatever variable you specified. If you want the second derivative, use this form `diff(expr, x\$2)`.

Exams in this course expect that you know and understand the use of the `diff` command. But, Maple has several other ways of for users to find the derivative. The other forms mentioned next will not be covered on exams. Be sure that you understand the meaning of the derivative and how its value is used to compute the solution you need.

A second approach is to enter the expression, then right-click the result, select the Differentiate option from the menu, and then select the variable with respect to which you want to differentiate. If you want the second derivative, repeat the process on the previous result, and so on for higher order derivatives.

Maple also understands the prime notation that is found in most Calculus books. Follow the expression or name of an expression with the prime (single quote `'`) character and Maple computes and returns the derivative of the expression.

Yet another way to get the derivative, is to click the Expression menu tab on the left menu in the Maple window. This will open the menu and show a lot of different mathematical operations. Select the $\frac{d}{dx}f$ from the menu and replace the x and the f with the variable and the expression you wish to differentiate.