Derivative with a fraction freaks me outI 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? :/

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Derivative with a fraction freaks me outI 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? :/

barbesdestyle2k · Accepted Answer

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

Derivative with a fraction freaks me out I have this: L ( μ ,

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