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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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{x - 1}(xx + Xx - 1)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}e^{x - 1} + Xxe^{x - 1} - e^{x - 1}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{2}e^{x - 1} + Xxe^{x - 1} - e^{x - 1}\right)}{dx}\\=&2xe^{x - 1} + x^{2}e^{x - 1}(1 + 0) + Xe^{x - 1} + Xxe^{x - 1}(1 + 0) - e^{x - 1}(1 + 0)\\=&2xe^{x - 1} + x^{2}e^{x - 1} + Xe^{x - 1} + Xxe^{x - 1} - e^{x - 1}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2xe^{x - 1} + x^{2}e^{x - 1} + Xe^{x - 1} + Xxe^{x - 1} - e^{x - 1}\right)}{dx}\\=&2e^{x - 1} + 2xe^{x - 1}(1 + 0) + 2xe^{x - 1} + x^{2}e^{x - 1}(1 + 0) + Xe^{x - 1}(1 + 0) + Xe^{x - 1} + Xxe^{x - 1}(1 + 0) - e^{x - 1}(1 + 0)\\=&e^{x - 1} + 4xe^{x - 1} + x^{2}e^{x - 1} + 2Xe^{x - 1} + Xxe^{x - 1}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( e^{x - 1} + 4xe^{x - 1} + x^{2}e^{x - 1} + 2Xe^{x - 1} + Xxe^{x - 1}\right)}{dx}\\=&e^{x - 1}(1 + 0) + 4e^{x - 1} + 4xe^{x - 1}(1 + 0) + 2xe^{x - 1} + x^{2}e^{x - 1}(1 + 0) + 2Xe^{x - 1}(1 + 0) + Xe^{x - 1} + Xxe^{x - 1}(1 + 0)\\=&5e^{x - 1} + 6xe^{x - 1} + x^{2}e^{x - 1} + 3Xe^{x - 1} + Xxe^{x - 1}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 5e^{x - 1} + 6xe^{x - 1} + x^{2}e^{x - 1} + 3Xe^{x - 1} + Xxe^{x - 1}\right)}{dx}\\=&5e^{x - 1}(1 + 0) + 6e^{x - 1} + 6xe^{x - 1}(1 + 0) + 2xe^{x - 1} + x^{2}e^{x - 1}(1 + 0) + 3Xe^{x - 1}(1 + 0) + Xe^{x - 1} + Xxe^{x - 1}(1 + 0)\\=&11e^{x - 1} + 8xe^{x - 1} + x^{2}e^{x - 1} + 4Xe^{x - 1} + Xxe^{x - 1}\\ \end{split}\end{equation} \]





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