Derivative of Square Root

  • Thread starter ssmh
  • Start date
  • #1
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I can't figure out
Derivative of (sq. rt of x)^x

Can anyone help me?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
djeitnstine
Gold Member
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Welcome to PF =]

Use the chain rule, this is simply a function within another function. the outer function just happens to be an exponential. [tex]\frac{d}{dx}f^x=f^x ln(f)[/tex] (if I remember correctly)
 
  • #3
327
1
if this is what you mean :

find f(x) prime, where f(x) = sqrt(x)^x

Before I help you, you need to help me. Tell me what concept you have learned that could
apply to this problem
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Welcome to PF =]

Use the chain rule, this is simply a function within another function. the outer function just happens to be an exponential. [tex]\frac{d}{dx}f^x=f^x ln(f)[/tex] (if I remember correctly)

No, that's incorrect.
 
  • #5
5
0
Here's how I did it.

[tex]\frac{d}{dx}[/tex](xx/2)

[tex]\frac{d}{dx}[/tex]e(x/2)ln(x)

(1/2)(1 + ln(x))e(xln(x))/2

[tex]\frac{1 + ln(x)}{2}[/tex] * x(x/2)
 
  • #6
239
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looks good to me.
 

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