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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x*4sin(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4xsin(x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( 4xsin(x)\right)}{dx}\\=&4sin(x) + 4xcos(x)\\=&4sin(x) + 4xcos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4sin(x) + 4xcos(x)\right)}{dx}\\=&4cos(x) + 4cos(x) + 4x*-sin(x)\\=&8cos(x) - 4xsin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 8cos(x) - 4xsin(x)\right)}{dx}\\=&8*-sin(x) - 4sin(x) - 4xcos(x)\\=&-12sin(x) - 4xcos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -12sin(x) - 4xcos(x)\right)}{dx}\\=&-12cos(x) - 4cos(x) - 4x*-sin(x)\\=&-16cos(x) + 4xsin(x)\\ \end{split}\end{equation} \]





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