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The Basic Rules

The Sum and Difference Rules

We now know how to find the derivative of the basic functions (f(x) = c, where c is a constant, xn, ln x, ex, sin x and cos x) and the derivative of a constant multiple of these functions. The sum and difference rules provide us with rules for finding the derivatives of the sums or differences of any of these basic functions and their constant multiples.


In words, these rules state that the derivative of one function added to another is the derivative of the first plus the derivative of the second and the derivative of one function minus another is the derivative of the first minus the derivative of the second. Both of these rules are frequently used and should be memorized. We will now take a look at how to use these rules.


Example 4

Study the following examples.



Exercise 4A

Each time you click "New Exercise" a new exercise will be given. Find the derivative and then click "Show me the answer" to compare you answer to the solution.


Exercise 4B

Find the provided derivatives. The following Excel or MATLAB notation is used in the provided answers:

     a*sin(x)      (a/b)*sin(x)
     a*cos(x)           (a/b)*cos(x)
     a*e^(x)      (a/b)*e^(x)
     a/x      a/(b*x)
     a*x^(n)      (a/b)*x^(n)






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