Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ th(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( th(x)\right)}{dx}\\=&(1 - th^{2}(x))\\=& - th^{2}(x) + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - th^{2}(x) + 1\right)}{dx}\\=& - 2th(x)(1 - th^{2}(x)) + 0\\=& - 2th(x) + 2th^{3}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2th(x) + 2th^{3}(x)\right)}{dx}\\=& - 2(1 - th^{2}(x)) + 2*3th^{2}(x)(1 - th^{2}(x))\\=&8th^{2}(x) - 6th^{4}(x) - 2\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 8th^{2}(x) - 6th^{4}(x) - 2\right)}{dx}\\=&8*2th(x)(1 - th^{2}(x)) - 6*4th^{3}(x)(1 - th^{2}(x)) + 0\\=&16th(x) - 40th^{3}(x) + 24th^{5}(x)\\ \end{split}\end{equation} \]





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