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Derivatives of square roots 
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#1
Apr1304, 06:52 PM

P: 5

How can i find the derivative of a function like this:
f(x) = sqrt( 1  x² ) 


#2
Apr1304, 06:57 PM

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Do you know how to write a square root with exponents?



#3
Apr1304, 07:02 PM

P: 5

(1  x² )^(1/2) ?



#4
Apr1304, 07:06 PM

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Derivatives of square roots
That's right! Now, you just need to apply what you know about differentiating expressions like that.



#5
Apr1304, 07:26 PM

P: 5

si will that be:
1/2((1x²)/2)^(1/2) ? 


#6
Apr1304, 07:56 PM

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Not quite. You have one too many "1/2"s (you don't want that "/2" inside the square root and you didn't use the chain rule.
You need to multiply by the derivative of 1x^{2}. 


#7
May1309, 08:58 AM

P: 2

Hi,
I have a similar problem, I need to differentiate sqrt(x^2 + y^2) in terms of x and y. Starting this I took the simple step (x^2 + y^2)^(1/2)... My next step is a guess and I am lost after it....(1/2)(x^2 + y^2)(1/2).... Any help would be much appreciated. 


#8
May1309, 10:26 AM

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#9
May1309, 10:40 AM

P: 2

thanks, would I do this by...
df/dx = 1/2(x^2 + y^2)^(1/2).2x = x/sqrt(x^2 + y^2) and... df/dy = 1/2(x^2 + y^2)^(1/2).2y = y/sqrt(x^2 + y^2) ? thanks for your help so quickly. 


#11
Jul1609, 11:50 AM

P: 2

What if i have a problem similar to these however now its 4/ ^5sqrt(x^5)



#12
Jul1709, 06:03 AM

P: 92

4^(5(x^(5/2)) And using what you know from differentiating exponentials and chain rule, you should be able to get the rest. 


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