# Derivatives of square roots

by the1024b
Tags: derivatives, roots, square
 P: 5 How can i find the derivative of a function like this: f(x) = sqrt( 1 - x² )
 Emeritus Sci Advisor PF Gold P: 16,091 Do you know how to write a square root with exponents?
 P: 5 (1 - x² )^(1/2) ?
 Emeritus Sci Advisor PF Gold P: 16,091 Derivatives of square roots That's right! Now, you just need to apply what you know about differentiating expressions like that.
 P: 5 si will that be: 1/2((1-x²)/2)^(-1/2) ?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 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 1-x2.
 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.
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PF Gold
P: 3,288
 Quote by mathsn00b 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.
If by "in terms of x and y", you mean you want to calculate the partial derivatives, then for the partial derivative with respect to x, treat y as a constant and differentiate with respect to x as you normally would a function of one variable. For the partial derivative with respect to y, treat x as constant.
 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.
HW Helper
PF Gold
P: 3,288
 Quote by mathsn00b 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.
Looks good to me.
 P: 2 What if i have a problem similar to these however now its 4/ ^5sqrt(x^5)
P: 92
 Quote by 68Pirate What if i have a problem similar to these however now its 4/ ^5sqrt(x^5)
If that is meant to be 4^(5(sqrt(x^5))), then you can easily rewrite this to equal
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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