What is the 10th derivative of f(x)=(3x^4 + 13x^2)^13?
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Given the function
,
the first derivative,
.
the second derivative,
.
the third derivative,
![Rendered by QuickLaTeX.com =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](https://acedstudy.com/wp-content/ql-cache/quicklatex.com-184e7423cab75ddf824a61ca32afe0b0_l3.png)
Continuing the differentiation up to the 10th degree gives you![Rendered by QuickLaTeX.com 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)](https://acedstudy.com/wp-content/ql-cache/quicklatex.com-b2a58ef5f0a6cb9a47ed8ea4942273cb_l3.png)
PS. I used software to get the 10th derivative.