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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 18sin(x) + 9xcos(x) - 4ccos(x) - 4csin(x) - 2cxcos(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 18sin(x) + 9xcos(x) - 4ccos(x) - 4csin(x) - 2cxcos(x)\right)}{dx}\\=&18cos(x) + 9cos(x) + 9x*-sin(x) - 4c*-sin(x) - 4ccos(x) - 2ccos(x) - 2cx*-sin(x)\\=&27cos(x) - 9xsin(x) + 4csin(x) - 6ccos(x) + 2cxsin(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 27cos(x) - 9xsin(x) + 4csin(x) - 6ccos(x) + 2cxsin(x)\right)}{dx}\\=&27*-sin(x) - 9sin(x) - 9xcos(x) + 4ccos(x) - 6c*-sin(x) + 2csin(x) + 2cxcos(x)\\=&-36sin(x) - 9xcos(x) + 4ccos(x) + 8csin(x) + 2cxcos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -36sin(x) - 9xcos(x) + 4ccos(x) + 8csin(x) + 2cxcos(x)\right)}{dx}\\=&-36cos(x) - 9cos(x) - 9x*-sin(x) + 4c*-sin(x) + 8ccos(x) + 2ccos(x) + 2cx*-sin(x)\\=&-45cos(x) + 9xsin(x) - 4csin(x) + 10ccos(x) - 2cxsin(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -45cos(x) + 9xsin(x) - 4csin(x) + 10ccos(x) - 2cxsin(x)\right)}{dx}\\=&-45*-sin(x) + 9sin(x) + 9xcos(x) - 4ccos(x) + 10c*-sin(x) - 2csin(x) - 2cxcos(x)\\=&54sin(x) + 9xcos(x) - 4ccos(x) - 12csin(x) - 2cxcos(x)\\ \end{split}\end{equation} \]





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