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 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ x(1 - cos(x))\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - xcos(x) + x\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( - xcos(x) + x\right)}{dx}\\=& - cos(x) - x*-sin(x) + 1\\=& - cos(x) + xsin(x) + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - cos(x) + xsin(x) + 1\right)}{dx}\\=& - -sin(x) + sin(x) + xcos(x) + 0\\=&2sin(x) + xcos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2sin(x) + xcos(x)\right)}{dx}\\=&2cos(x) + cos(x) + x*-sin(x)\\=&3cos(x) - xsin(x)\\ \end{split}\end{equation} \]





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