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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (x + 1)({x}^{2} - 4x + 16)({x}^{2} + {1}^{2} - 4)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5} - 3x^{4} + 9x^{3} + 25x^{2} - 36x - 48\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{5} - 3x^{4} + 9x^{3} + 25x^{2} - 36x - 48\right)}{dx}\\=&5x^{4} - 3*4x^{3} + 9*3x^{2} + 25*2x - 36 + 0\\=&5x^{4} - 12x^{3} + 27x^{2} + 50x - 36\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 5x^{4} - 12x^{3} + 27x^{2} + 50x - 36\right)}{dx}\\=&5*4x^{3} - 12*3x^{2} + 27*2x + 50 + 0\\=&20x^{3} - 36x^{2} + 54x + 50\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 20x^{3} - 36x^{2} + 54x + 50\right)}{dx}\\=&20*3x^{2} - 36*2x + 54 + 0\\=&60x^{2} - 72x + 54\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 60x^{2} - 72x + 54\right)}{dx}\\=&60*2x - 72 + 0\\=&120x - 72\\ \end{split}\end{equation} \]





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