There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(x + y + z)}^{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x + y + z)^{6}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x + y + z)^{6}\right)}{dx}\\=&(6(x + y + z)^{5}(1 + 0 + 0))\\=&6x^{5} + 30yx^{4} + 30zx^{4} + 60y^{2}x^{3} + 120yzx^{3} + 60z^{2}x^{3} + 60y^{3}x^{2} + 180y^{2}zx^{2} + 180yz^{2}x^{2} + 60z^{3}x^{2} + 30y^{4}x + 120y^{3}zx + 180y^{2}z^{2}x + 120yz^{3}x + 30z^{4}x + 30y^{4}z + 60y^{3}z^{2} + 60y^{2}z^{3} + 30yz^{4} + 6y^{5} + 6z^{5}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 6x^{5} + 30yx^{4} + 30zx^{4} + 60y^{2}x^{3} + 120yzx^{3} + 60z^{2}x^{3} + 60y^{3}x^{2} + 180y^{2}zx^{2} + 180yz^{2}x^{2} + 60z^{3}x^{2} + 30y^{4}x + 120y^{3}zx + 180y^{2}z^{2}x + 120yz^{3}x + 30z^{4}x + 30y^{4}z + 60y^{3}z^{2} + 60y^{2}z^{3} + 30yz^{4} + 6y^{5} + 6z^{5}\right)}{dx}\\=&6*5x^{4} + 30y*4x^{3} + 30z*4x^{3} + 60y^{2}*3x^{2} + 120yz*3x^{2} + 60z^{2}*3x^{2} + 60y^{3}*2x + 180y^{2}z*2x + 180yz^{2}*2x + 60z^{3}*2x + 30y^{4} + 120y^{3}z + 180y^{2}z^{2} + 120yz^{3} + 30z^{4} + 0 + 0 + 0 + 0 + 0 + 0\\=&30x^{4} + 120yx^{3} + 120zx^{3} + 180y^{2}x^{2} + 360yzx^{2} + 180z^{2}x^{2} + 120y^{3}x + 360y^{2}zx + 360yz^{2}x + 120z^{3}x + 120y^{3}z + 180y^{2}z^{2} + 120yz^{3} + 30y^{4} + 30z^{4}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 30x^{4} + 120yx^{3} + 120zx^{3} + 180y^{2}x^{2} + 360yzx^{2} + 180z^{2}x^{2} + 120y^{3}x + 360y^{2}zx + 360yz^{2}x + 120z^{3}x + 120y^{3}z + 180y^{2}z^{2} + 120yz^{3} + 30y^{4} + 30z^{4}\right)}{dx}\\=&30*4x^{3} + 120y*3x^{2} + 120z*3x^{2} + 180y^{2}*2x + 360yz*2x + 180z^{2}*2x + 120y^{3} + 360y^{2}z + 360yz^{2} + 120z^{3} + 0 + 0 + 0 + 0 + 0\\=&120x^{3} + 360yx^{2} + 360zx^{2} + 360y^{2}x + 720yzx + 360z^{2}x + 360y^{2}z + 360yz^{2} + 120y^{3} + 120z^{3}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 120x^{3} + 360yx^{2} + 360zx^{2} + 360y^{2}x + 720yzx + 360z^{2}x + 360y^{2}z + 360yz^{2} + 120y^{3} + 120z^{3}\right)}{dx}\\=&120*3x^{2} + 360y*2x + 360z*2x + 360y^{2} + 720yz + 360z^{2} + 0 + 0 + 0 + 0\\=&360x^{2} + 720yx + 720zx + 720yz + 360y^{2} + 360z^{2}\\ \end{split}\end{equation} \]

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