There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln({4}^{{(11x)}^{{(3x)}^{2}}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln({4}^{(11x)^{(9x^{2})}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln({4}^{(11x)^{(9x^{2})}})\right)}{dx}\\=&\frac{({4}^{(11x)^{(9x^{2})}}((((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)})))ln(4) + \frac{((11x)^{(9x^{2})})(0)}{(4)}))}{({4}^{(11x)^{(9x^{2})}})}\\=&18x(11x)^{(9x^{2})}ln(11x)ln(4) + 9x(11x)^{(9x^{2})}ln(4)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 18x(11x)^{(9x^{2})}ln(11x)ln(4) + 9x(11x)^{(9x^{2})}ln(4)\right)}{dx}\\=&18(11x)^{(9x^{2})}ln(11x)ln(4) + 18x((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(11x)ln(4) + \frac{18x(11x)^{(9x^{2})}*11ln(4)}{(11x)} + \frac{18x(11x)^{(9x^{2})}ln(11x)*0}{(4)} + 9(11x)^{(9x^{2})}ln(4) + 9x((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(4) + \frac{9x(11x)^{(9x^{2})}*0}{(4)}\\=&18(11x)^{(9x^{2})}ln(11x)ln(4) + 324x^{2}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 324x^{2}(11x)^{(9x^{2})}ln(11x)ln(4) + 27(11x)^{(9x^{2})}ln(4) + 81x^{2}(11x)^{(9x^{2})}ln(4)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 18(11x)^{(9x^{2})}ln(11x)ln(4) + 324x^{2}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 324x^{2}(11x)^{(9x^{2})}ln(11x)ln(4) + 27(11x)^{(9x^{2})}ln(4) + 81x^{2}(11x)^{(9x^{2})}ln(4)\right)}{dx}\\=&18((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(11x)ln(4) + \frac{18(11x)^{(9x^{2})}*11ln(4)}{(11x)} + \frac{18(11x)^{(9x^{2})}ln(11x)*0}{(4)} + 324*2x(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 324x^{2}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln^{2}(11x)ln(4) + \frac{324x^{2}(11x)^{(9x^{2})}*2ln(11x)*11ln(4)}{(11x)} + \frac{324x^{2}(11x)^{(9x^{2})}ln^{2}(11x)*0}{(4)} + 324*2x(11x)^{(9x^{2})}ln(11x)ln(4) + 324x^{2}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(11x)ln(4) + \frac{324x^{2}(11x)^{(9x^{2})}*11ln(4)}{(11x)} + \frac{324x^{2}(11x)^{(9x^{2})}ln(11x)*0}{(4)} + 27((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(4) + \frac{27(11x)^{(9x^{2})}*0}{(4)} + 81*2x(11x)^{(9x^{2})}ln(4) + 81x^{2}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(4) + \frac{81x^{2}(11x)^{(9x^{2})}*0}{(4)}\\=&972x(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 1944x(11x)^{(9x^{2})}ln(11x)ln(4) + 5832x^{3}(11x)^{(9x^{2})}ln^{3}(11x)ln(4) + 8748x^{3}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 4374x^{3}(11x)^{(9x^{2})}ln(11x)ln(4) + \frac{18(11x)^{(9x^{2})}ln(4)}{x} + 729x(11x)^{(9x^{2})}ln(4) + 729x^{3}(11x)^{(9x^{2})}ln(4)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 972x(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 1944x(11x)^{(9x^{2})}ln(11x)ln(4) + 5832x^{3}(11x)^{(9x^{2})}ln^{3}(11x)ln(4) + 8748x^{3}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 4374x^{3}(11x)^{(9x^{2})}ln(11x)ln(4) + \frac{18(11x)^{(9x^{2})}ln(4)}{x} + 729x(11x)^{(9x^{2})}ln(4) + 729x^{3}(11x)^{(9x^{2})}ln(4)\right)}{dx}\\=&972(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 972x((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln^{2}(11x)ln(4) + \frac{972x(11x)^{(9x^{2})}*2ln(11x)*11ln(4)}{(11x)} + \frac{972x(11x)^{(9x^{2})}ln^{2}(11x)*0}{(4)} + 1944(11x)^{(9x^{2})}ln(11x)ln(4) + 1944x((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(11x)ln(4) + \frac{1944x(11x)^{(9x^{2})}*11ln(4)}{(11x)} + \frac{1944x(11x)^{(9x^{2})}ln(11x)*0}{(4)} + 5832*3x^{2}(11x)^{(9x^{2})}ln^{3}(11x)ln(4) + 5832x^{3}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln^{3}(11x)ln(4) + \frac{5832x^{3}(11x)^{(9x^{2})}*3ln^{2}(11x)*11ln(4)}{(11x)} + \frac{5832x^{3}(11x)^{(9x^{2})}ln^{3}(11x)*0}{(4)} + 8748*3x^{2}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 8748x^{3}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln^{2}(11x)ln(4) + \frac{8748x^{3}(11x)^{(9x^{2})}*2ln(11x)*11ln(4)}{(11x)} + \frac{8748x^{3}(11x)^{(9x^{2})}ln^{2}(11x)*0}{(4)} + 4374*3x^{2}(11x)^{(9x^{2})}ln(11x)ln(4) + 4374x^{3}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(11x)ln(4) + \frac{4374x^{3}(11x)^{(9x^{2})}*11ln(4)}{(11x)} + \frac{4374x^{3}(11x)^{(9x^{2})}ln(11x)*0}{(4)} + \frac{18*-(11x)^{(9x^{2})}ln(4)}{x^{2}} + \frac{18((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(4)}{x} + \frac{18(11x)^{(9x^{2})}*0}{x(4)} + 729(11x)^{(9x^{2})}ln(4) + 729x((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(4) + \frac{729x(11x)^{(9x^{2})}*0}{(4)} + 729*3x^{2}(11x)^{(9x^{2})}ln(4) + 729x^{3}((11x)^{(9x^{2})}((9*2x)ln(11x) + \frac{(9x^{2})(11)}{(11x)}))ln(4) + \frac{729x^{3}(11x)^{(9x^{2})}*0}{(4)}\\=&972(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 34992x^{2}(11x)^{(9x^{2})}ln^{3}(11x)ln(4) + 87480x^{2}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 4212(11x)^{(9x^{2})}ln(11x)ln(4) + 104976x^{4}(11x)^{(9x^{2})}ln^{4}(11x)ln(4) + 209952x^{4}(11x)^{(9x^{2})}ln^{3}(11x)ln(4) + 2835(11x)^{(9x^{2})}ln(4) + 157464x^{4}(11x)^{(9x^{2})}ln^{2}(11x)ln(4) + 61236x^{2}(11x)^{(9x^{2})}ln(11x)ln(4) + 52488x^{4}(11x)^{(9x^{2})}ln(11x)ln(4) + 13122x^{2}(11x)^{(9x^{2})}ln(4) - \frac{18(11x)^{(9x^{2})}ln(4)}{x^{2}} + 6561x^{4}(11x)^{(9x^{2})}ln(4)\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！