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donggela
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Tyro
Asked: 2021-04-06T13:39:09+00:00 In: ,

Finding Derivative

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What is the 10th derivative of f(x)=(3x^4 + 13x^2)^13?

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  2. acedstud
    This answer was edited.

    Given the function f(x)=(3x^4 + 13x^2)^{13},

    the first derivative, f'(x)=13(3x^4+13x^2)^{12}(12x^3+26x).

    the second derivative, f''(x)=13(3x^4+13x^2)^{12}(36x^2+26)+156(3x^4+13x^2)^{11}(12x^3+26x)^2.

    the third derivative, f'''(x)=13(3x^4+13x^2)^{12}(72x)+156(3x^4+13x^2)^{11}(12x^3+26x)(36x^2+26)+156(3x^4+13x^2)^{11}\cdot2(12x^3+26x)(36x^2+26)+1716(3x^4+13x^2)^{10}(12x^3+26x)^2 =936x(3x^4+13x^2)^{12}+468(3x^4+13x^2)^{11}(12x^3+26x)(36x^2+26)+1716(3x^4+13x^2)^{10}(12x^3+26x)^2 =936x(3x^4+13x^2)^{12}+468(3x^4+13x^2)^{11}(432x^5+1248x^3+676x)+1716(3x^4+13x^2)^{10}(12x^3+26x)^2

     

    Continuing the differentiation up to the 10th degree gives you f^{(10)}(x) = 518918400 x^{16} (3 x^2 + 13)^3 (6532563707460 x^{20} + 154027605063150 x^{18} + 1585497128195214 x^{16} + 9352506747535146 x^{14} + 34878643068019140 x^{12} + 85545143980134111 x^{10} + 138999556616143275 x^8 + 146797397096692680 x^6 + 95675645051942670 x^4 + 34408684228057425 x^2 + 5120753679731105)

     

    PS. I used software to get the 10th derivative.

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