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# microbook_3e-page20 - 5 x h x 3 x 3 x g x 2 x f 1 2 then 5...

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the power-function rule Now if the value of x in the function + , x f is raised to a power (i.e. it has an exponent), then all we have to do to find the derivative is “roll the exponent over.” To roll the exponent over, multiply the original function by the original exponent and subtract one from the original exponent. For example: + , + , + , 2 3 x 15 x f x d x f d x 5 x f c 2 1 3 3 x 15 x 5 3 x 5 ¡ o 0 + , + , + , x 2 x 2 x g x d x g d x 4 x 4 x g 2 1 2 1 c 0 2 1 1 2 1 2 1 x 2 x 4 2 1 x 4 0 0 ¡ o the sum-difference rule Now, say the function you are considering contains the variable x in two or more terms. + , 5 x 3 x 2 x k 2 . 0 if we define: + ,
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Unformatted text preview: 5 x h x 3 x 3 x g x 2 x f 1 2 then: + , + , + , + , 5 x 3 x 2 x h x g x f x k 2 . . . Now we can just take the derivatives of + , x f , + , x g and + , x h and then add up the individual derivatives to find + , x k c . After all, the change in a sum is equal to the sum of the changes. + , + , + , + , + , + , + , + , + , 3 x 4 x 3 1 x 2 2 x k x h x g x f x k x d x h d x d x g d x d x f d x d x k d 1 1 1 2 . ¡ ¡ c c . c . c c . . Page 20...
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