Power rule

  • #1
145
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Homework Statement


I promise this will be my last one :p

For this function: [tex]f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2[/tex]
What would be the derivative using the power rule?


Homework Equations



[tex]f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2[/tex]

The Attempt at a Solution



[tex]f'(x)=-12x^{2}-3x^{-2}-\frac{\sqrt{x}}{2}[/tex]

However, this is wrong. Why?
 

Answers and Replies

  • #2
867
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[tex]\sqrt{x} = x^\frac{1}{2}[/tex]

Use the power rule and subtract one from that exponent.
 
  • #3
145
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[tex]f'(x)=-12x^{2}-3x^{-2}+\frac{1}{2x^{1/2}}[/tex]

1/2 - 1 = -1/2
 
  • #4
12
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derivative of x^1/2 = 1/2 x^(-1/2)
 
  • #5
867
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The exponent is -1/2, but that term should be positive.
 
  • #6
145
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derivative of x^1/2 = 1/2 x^(-1/2)

Could that be written as [tex]\frac{1}{2\sqrt{x}}[/tex]?
 
  • #7
145
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The exponent is -1/2, but that term should be positive.

[tex]f'(x)=-12x^{2}-3x^{-2}+\frac{1}{2x^{1/2}}[/tex]

Like this?
 
  • #8
867
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Yes, that's right. Didn't see your other post with the correct answer.
 
  • #9
145
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Yes, that's right. Didn't see your other post with the correct answer.

I edited it :D
I was just wondering because the book has a much different answer :/
 
  • #10
867
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What does the book say?
 

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