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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{{x}^{5}}{12} + xcos(x) - 3sin(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = xcos(x) + \frac{1}{12}x^{5} - 3sin(x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( xcos(x) + \frac{1}{12}x^{5} - 3sin(x)\right)}{dx}\\=&cos(x) + x*-sin(x) + \frac{1}{12}*5x^{4} - 3cos(x)\\=& - 2cos(x) - xsin(x) + \frac{5x^{4}}{12}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2cos(x) - xsin(x) + \frac{5x^{4}}{12}\right)}{dx}\\=& - 2*-sin(x) - sin(x) - xcos(x) + \frac{5*4x^{3}}{12}\\=&sin(x) - xcos(x) + \frac{5x^{3}}{3}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( sin(x) - xcos(x) + \frac{5x^{3}}{3}\right)}{dx}\\=&cos(x) - cos(x) - x*-sin(x) + \frac{5*3x^{2}}{3}\\=&xsin(x) + 5x^{2}\\ \end{split}\end{equation} \]





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