derivative of a square root First we convert the square root to exponent notation frac d dx sqrt f x frac d dx f x frac 1 2 Then take the derivative and apply the chain rule That exponent is frac 1 2 for some reason the markup language is making it hard to see the negative sign frac 1 2 f x frac 1 2 f x
That is the derivative of this local square root at identity is frac12 T endgroup ronno A QS where Q is an orthogonal matrix and S is defined uniquely as precisely what you describe above when it exists Hence what you really want to calculate is S A Q 1A A Q 1 I Note the result is a fourth order linear transformation since we are the describing the rate of change of a second order object S
derivative of a square root
derivative of a square root
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I know I ll have to apply the chain rule here but with the sum and the square root I am unsure of the correct order of the steps multivariable calculus derivatives Derivative with a Square root in Denominator Ask Question Asked 10 years 7 months ago Modified 10 years
begingroup I would like an expression in terms of the non square root derivative partial Omega i X Omega I am interested in results for both real and Hermitian matrices I will edit my question to say this endgroup Let A be a square symmetric positive definite matrix Let S be its symmetric square root found by a singular value decomposition Let vech be the half vectorization operator Is there a convenient expression for the derivative or differential of vech S with respect to vech A
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