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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (x + 1)({x}^{2} - 4x + 16)(x + {1}^{2} - 4)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{4} - 6x^{3} + 21x^{2} - 20x - 48\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{4} - 6x^{3} + 21x^{2} - 20x - 48\right)}{dx}\\=&4x^{3} - 6*3x^{2} + 21*2x - 20 + 0\\=&4x^{3} - 18x^{2} + 42x - 20\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4x^{3} - 18x^{2} + 42x - 20\right)}{dx}\\=&4*3x^{2} - 18*2x + 42 + 0\\=&12x^{2} - 36x + 42\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12x^{2} - 36x + 42\right)}{dx}\\=&12*2x - 36 + 0\\=&24x - 36\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24x - 36\right)}{dx}\\=&24 + 0\\=&24\\ \end{split}\end{equation} \]





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