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Differentiation help

  • #1


Could someone help me with this simple differentiation?
u= 5root(1/x^8)
--> =(1/x^8)^1/5
= (1/5)/(x^8/5)
du/dx= ?
I don't know what to do after here, as I keep getting the wrong answer.
The answer is du/dx = (-8/5)x^-13/5
:( Thanks!!
 
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Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
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Let's clarify the question. Do you want to differentiate

[tex]u=\Big({\frac{1}{x^8}}\Big)^{1/5}=x^{-8/5}[/tex]

What's the derivative of x^n wrt x?
 
  • #3
Yes. I want to differentiate that. How did you get to x^-8/5? I would know how to go from there, as its just reducing the power by one, and mutiplying the coefficient (1) by -8/5.
Thankyou for moving my question by the way! You have been really helpful so far!
 
  • #4
Two rules:

[tex]\left(x^a\right)^b=x^{ab}[/tex]

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Putting these together with your problem:
[tex]\left(\frac{1}{x^8}\right)^{1/5}=\left(x^{-8}\right)^{1/5}=x^{-8\times(1/5)}=x^{-8/5}.[/tex]

Now, using the differentiation rule as you have already worked out:
[tex]\frac{d}{dx}x^{-8/5}=-\frac{8}{5}x^{-13/5}[/tex]
 
  • #5
cristo
Staff Emeritus
Science Advisor
8,107
73
Yes. I want to differentiate that. How did you get to x^-8/5?
Sorry, I should've been more explicit there. See ubiquitousuk's detailed post.

Thankyou for moving my question by the way! You have been really helpful so far!
You're welcome.
 
  • #6
Two rules:

[tex]\left(x^a\right)^b=x^{ab}[/tex]

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Putting these together with your problem:
[tex]\left(\frac{1}{x^8}\right)^{1/5}=\left(x^{-8}\right)^{1/5}=x^{-8\times(1/5)}=x^{-8/5}.[/tex]

Now, using the differentiation rule as you have already worked out:
[tex]\frac{d}{dx}x^{-8/5}=-\frac{8}{5}x^{-13/5}[/tex]
Ah!!! Seems so simple now! Really helpful! Thanks!
 

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