There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {a}^{x} - {a}^{sin(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {a}^{x} - {a}^{sin(x)}\right)}{dx}\\=&({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)})) - ({a}^{sin(x)}((cos(x))ln(a) + \frac{(sin(x))(0)}{(a)}))\\=& - {a}^{sin(x)}ln(a)cos(x) + {a}^{x}ln(a)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - {a}^{sin(x)}ln(a)cos(x) + {a}^{x}ln(a)\right)}{dx}\\=& - ({a}^{sin(x)}((cos(x))ln(a) + \frac{(sin(x))(0)}{(a)}))ln(a)cos(x) - \frac{{a}^{sin(x)}*0cos(x)}{(a)} - {a}^{sin(x)}ln(a)*-sin(x) + ({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln(a) + \frac{{a}^{x}*0}{(a)}\\=& - {a}^{sin(x)}ln^{2}(a)cos^{2}(x) + {a}^{sin(x)}ln(a)sin(x) + {a}^{x}ln^{2}(a)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - {a}^{sin(x)}ln^{2}(a)cos^{2}(x) + {a}^{sin(x)}ln(a)sin(x) + {a}^{x}ln^{2}(a)\right)}{dx}\\=& - ({a}^{sin(x)}((cos(x))ln(a) + \frac{(sin(x))(0)}{(a)}))ln^{2}(a)cos^{2}(x) - \frac{{a}^{sin(x)}*2ln(a)*0cos^{2}(x)}{(a)} - {a}^{sin(x)}ln^{2}(a)*-2cos(x)sin(x) + ({a}^{sin(x)}((cos(x))ln(a) + \frac{(sin(x))(0)}{(a)}))ln(a)sin(x) + \frac{{a}^{sin(x)}*0sin(x)}{(a)} + {a}^{sin(x)}ln(a)cos(x) + ({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln^{2}(a) + \frac{{a}^{x}*2ln(a)*0}{(a)}\\=& - {a}^{sin(x)}ln^{3}(a)cos^{3}(x) + 3{a}^{sin(x)}ln^{2}(a)sin(x)cos(x) + {a}^{sin(x)}ln(a)cos(x) + {a}^{x}ln^{3}(a)\\ \end{split}\end{equation} \]

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