There are 1 questions in this calculation: for each question, the 4 derivative of a is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {a}^{b} + sin(a)(cos(b))\ with\ respect\ to\ a：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {a}^{b} + sin(a)cos(b)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {a}^{b} + sin(a)cos(b)\right)}{da}\\=&({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)})) + cos(a)cos(b) + sin(a)*-sin(b)*0\\=&\frac{b{a}^{b}}{a} + cos(a)cos(b)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{b{a}^{b}}{a} + cos(a)cos(b)\right)}{da}\\=&\frac{b*-{a}^{b}}{a^{2}} + \frac{b({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)}))}{a} + -sin(a)cos(b) + cos(a)*-sin(b)*0\\=&\frac{-b{a}^{b}}{a^{2}} + \frac{b^{2}{a}^{b}}{a^{2}} - sin(a)cos(b)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-b{a}^{b}}{a^{2}} + \frac{b^{2}{a}^{b}}{a^{2}} - sin(a)cos(b)\right)}{da}\\=&\frac{-b*-2{a}^{b}}{a^{3}} - \frac{b({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)}))}{a^{2}} + \frac{b^{2}*-2{a}^{b}}{a^{3}} + \frac{b^{2}({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)}))}{a^{2}} - cos(a)cos(b) - sin(a)*-sin(b)*0\\=&\frac{2b{a}^{b}}{a^{3}} - \frac{3b^{2}{a}^{b}}{a^{3}} + \frac{b^{3}{a}^{b}}{a^{3}} - cos(a)cos(b)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2b{a}^{b}}{a^{3}} - \frac{3b^{2}{a}^{b}}{a^{3}} + \frac{b^{3}{a}^{b}}{a^{3}} - cos(a)cos(b)\right)}{da}\\=&\frac{2b*-3{a}^{b}}{a^{4}} + \frac{2b({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)}))}{a^{3}} - \frac{3b^{2}*-3{a}^{b}}{a^{4}} - \frac{3b^{2}({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)}))}{a^{3}} + \frac{b^{3}*-3{a}^{b}}{a^{4}} + \frac{b^{3}({a}^{b}((0)ln(a) + \frac{(b)(1)}{(a)}))}{a^{3}} - -sin(a)cos(b) - cos(a)*-sin(b)*0\\=&\frac{-6b{a}^{b}}{a^{4}} + \frac{11b^{2}{a}^{b}}{a^{4}} - \frac{6b^{3}{a}^{b}}{a^{4}} + \frac{b^{4}{a}^{b}}{a^{4}} + sin(a)cos(b)\\ \end{split}\end{equation} \]

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