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





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