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             b) If ƒ(x)=0, then ƒ'(x)=0.
             c) If y=2, then dy/dx=0.
             d) If g(t)=(-3/2), then g'(t)=0.

Before deriving the next rule, we review the procedure for expanding a binomial. Recall that

           


And in general , the binomial expansion is

           


Where n is a positive integer. We use this binomial expansion in proving a special case of the following rule:



           
The four problems in Example 2 are very simple, yet error are frequently made in differentiating a constant multiple of the first power of x. keep in mind that

           where c is constant

The next rule is one that we can certainly would expectto be true and it is often used without thinking about it.For instance,if you where to find the derivative of y=3x+2x3 You would probably write

                      y’=3+6x2

Without questioning your answer. The validity of differentiating a sum "term bt term" is giving in the following rule.



If ƒ(x)=x3-4x+5,find the value of ƒ’(2).

Solution
ƒ’(x)=3x2-4. Therfore

ƒ’(2)=3(2)2-4=12-4=8


If y=3x-2,find the value of dy/dx when x=2.

Solution
By the Power Rule with n=-2,we obtain

           Therefore, when x=2