Derivative with a fraction freaks me out I have this: L ( &#x03BC;<!-- μ --> ,

hughy46u

hughy46u

Answered question

2022-05-30

Derivative with a fraction freaks me out
I have this:
L ( μ , σ 2 ) = 1 2 σ 2 n = 1 N ( x n μ ) 2
and I need to end up here:
σ 2 L ( μ , σ 2 ) = 1 2 σ 4 n = 1 N ( x n μ ) 2
But when I try to work things out, I do:
L ( μ , σ 2 ) = 2 1 ( σ 2 ) 1 n = 1 N ( x n μ ) 2 = 2 1 n = 1 N ( x n μ ) 2 ( σ 2 ) 1
thus
σ 2 L ( μ , σ 2 ) = 1 2 n = 1 N ( x n μ ) 2   σ 2
What am I missing? :/

Answer & Explanation

barbesdestyle2k

barbesdestyle2k

Beginner2022-05-31Added 10 answers

Think 2 1 n = 1 N ( x n μ ) 2 is just a multiplier of σ 2 and notice σ 2 σ 2 = ( 1 ) ( σ 2 ) 2
So you get σ 2 L ( μ , σ 2 ) = 2 1 ( n = 1 N ( x n μ ) 2 ) ( 1 ) ( σ 2 ) 2 = 1 2 σ 4 n = 1 N ( x n μ ) 2

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