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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Differentiation > Symbolic differentiation





http://functions.wolfram.com/01.20.20.0014.01









  


  










Input Form





D[Cosh[z]^m, {z, n}] == Sum[Binomial[m, k] (2 k - m)^n ((1 + (-1)^n) Sum[Binomial[m - 2 k, 2 j] Sinh[z]^(2 j) Cosh[z]^(m - 2 k - 2 j), {j, 0, Floor[m/2] - k}] - (1 - (-1)^n) Sum[Binomial[m - 2 k, 2 j + 1] Sinh[z]^(2 j + 1) Cosh[z]^(m - 2 k - 2 j - 1), {j, 0, Floor[(m - 1)/2] - k}]), {k, 0, Floor[(m - 1)/2]}]/2^m /; Element[m, Integers] && m >= 0 && Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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