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How do you find the first derivative of x^3(x+2)(x-4)?

 Apr 5, 2015

Best Answer 

 #1
avatar+130511 
+5

f(x ) = x^3(x+2)(x-4)

We could use the product/power rules, but I find just expanding this and using the power rule by itself is easier.

So we have

f(x) = x^3(x^2 - 2x - 8)  =  x^5 - 2x^4 - 8x^3

And 

f ' (x) =  5x^4 - 8x^3 - 24x^2

 

  

 Apr 5, 2015
 #1
avatar+130511 
+5
Best Answer

f(x ) = x^3(x+2)(x-4)

We could use the product/power rules, but I find just expanding this and using the power rule by itself is easier.

So we have

f(x) = x^3(x^2 - 2x - 8)  =  x^5 - 2x^4 - 8x^3

And 

f ' (x) =  5x^4 - 8x^3 - 24x^2

 

  

CPhill Apr 5, 2015

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