本次共计算 1 个题目：每一题对 x 求 4 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(48{ln(x)}^{2} + 384{y}^{2}{ln(x)}^{3} + 256{y}^{4}{ln(x)}^{4}){x}^{(2{y}^{2} + 3)} + {y}^{(x - 4)}({x}^{4} - 6{x}^{3} + 11{x}^{2} - 6x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 48{x}^{(2y^{2} + 3)}ln^{2}(x) + 384y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x) + 256y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x) + x^{4}{y}^{(x - 4)} - 6x^{3}{y}^{(x - 4)} + 11x^{2}{y}^{(x - 4)} - 6x{y}^{(x - 4)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 48{x}^{(2y^{2} + 3)}ln^{2}(x) + 384y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x) + 256y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x) + x^{4}{y}^{(x - 4)} - 6x^{3}{y}^{(x - 4)} + 11x^{2}{y}^{(x - 4)} - 6x{y}^{(x - 4)}\right)}{dx}\\=&48({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x) + \frac{48{x}^{(2y^{2} + 3)}*2ln(x)}{(x)} + 384y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x) + \frac{384y^{2}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{(x)} + 256y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x) + \frac{256y^{4}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{(x)} + 4x^{3}{y}^{(x - 4)} + x^{4}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) - 6*3x^{2}{y}^{(x - 4)} - 6x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) + 11*2x{y}^{(x - 4)} + 11x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) - 6{y}^{(x - 4)} - 6x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))\\=&\frac{1248y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x} + \frac{144{x}^{(2y^{2} + 3)}ln^{2}(x)}{x} + \frac{96{x}^{(2y^{2} + 3)}ln(x)}{x} + \frac{1792y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x} + \frac{1152y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x} + \frac{512y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x} + \frac{768y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x} + x^{4}{y}^{(x - 4)}ln(y) - 6x^{3}{y}^{(x - 4)}ln(y) + 11x^{2}{y}^{(x - 4)}ln(y) - 6x{y}^{(x - 4)}ln(y) + 22x{y}^{(x - 4)} - 18x^{2}{y}^{(x - 4)} - 6{y}^{(x - 4)} + 4x^{3}{y}^{(x - 4)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1248y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x} + \frac{144{x}^{(2y^{2} + 3)}ln^{2}(x)}{x} + \frac{96{x}^{(2y^{2} + 3)}ln(x)}{x} + \frac{1792y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x} + \frac{1152y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x} + \frac{512y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x} + \frac{768y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x} + x^{4}{y}^{(x - 4)}ln(y) - 6x^{3}{y}^{(x - 4)}ln(y) + 11x^{2}{y}^{(x - 4)}ln(y) - 6x{y}^{(x - 4)}ln(y) + 22x{y}^{(x - 4)} - 18x^{2}{y}^{(x - 4)} - 6{y}^{(x - 4)} + 4x^{3}{y}^{(x - 4)}\right)}{dx}\\=&\frac{1248y^{2}*-{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{1248y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x} + \frac{1248y^{2}{x}^{(2y^{2} + 3)}*2ln(x)}{x(x)} + \frac{144*-{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{144({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x} + \frac{144{x}^{(2y^{2} + 3)}*2ln(x)}{x(x)} + \frac{96*-{x}^{(2y^{2} + 3)}ln(x)}{x^{2}} + \frac{96({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln(x)}{x} + \frac{96{x}^{(2y^{2} + 3)}}{x(x)} + \frac{1792y^{4}*-{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{1792y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x} + \frac{1792y^{4}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x(x)} + \frac{1152y^{2}*-{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{1152y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x} + \frac{1152y^{2}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x(x)} + \frac{512y^{6}*-{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} + \frac{512y^{6}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x} + \frac{512y^{6}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x(x)} + \frac{768y^{4}*-{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} + \frac{768y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x} + \frac{768y^{4}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x(x)} + 4x^{3}{y}^{(x - 4)}ln(y) + x^{4}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) + \frac{x^{4}{y}^{(x - 4)}*0}{(y)} - 6*3x^{2}{y}^{(x - 4)}ln(y) - 6x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) - \frac{6x^{3}{y}^{(x - 4)}*0}{(y)} + 11*2x{y}^{(x - 4)}ln(y) + 11x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) + \frac{11x^{2}{y}^{(x - 4)}*0}{(y)} - 6{y}^{(x - 4)}ln(y) - 6x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) - \frac{6x{y}^{(x - 4)}*0}{(y)} + 22{y}^{(x - 4)} + 22x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) - 18*2x{y}^{(x - 4)} - 18x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) - 6({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) + 4*3x^{2}{y}^{(x - 4)} + 4x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))\\=&\frac{6240y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{7872y^{4}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{2688y^{2}{x}^{(2y^{2} + 3)}ln(x)}{x^{2}} + \frac{288{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{480{x}^{(2y^{2} + 3)}ln(x)}{x^{2}} + 8x^{3}{y}^{(x - 4)}ln(y) + \frac{8960y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{5632y^{6}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{2304y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{2560y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} + \frac{1024y^{8}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} + \frac{1536y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} - 36x^{2}{y}^{(x - 4)}ln(y) + x^{4}{y}^{(x - 4)}ln^{2}(y) + 44x{y}^{(x - 4)}ln(y) - 6x^{3}{y}^{(x - 4)}ln^{2}(y) + 11x^{2}{y}^{(x - 4)}ln^{2}(y) - 6x{y}^{(x - 4)}ln^{2}(y) - 12{y}^{(x - 4)}ln(y) + \frac{96{x}^{(2y^{2} + 3)}}{x^{2}} + 22{y}^{(x - 4)} - 36x{y}^{(x - 4)} + 12x^{2}{y}^{(x - 4)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{6240y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{7872y^{4}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{2688y^{2}{x}^{(2y^{2} + 3)}ln(x)}{x^{2}} + \frac{288{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{2}} + \frac{480{x}^{(2y^{2} + 3)}ln(x)}{x^{2}} + 8x^{3}{y}^{(x - 4)}ln(y) + \frac{8960y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{5632y^{6}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{2304y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{2}} + \frac{2560y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} + \frac{1024y^{8}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} + \frac{1536y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{2}} - 36x^{2}{y}^{(x - 4)}ln(y) + x^{4}{y}^{(x - 4)}ln^{2}(y) + 44x{y}^{(x - 4)}ln(y) - 6x^{3}{y}^{(x - 4)}ln^{2}(y) + 11x^{2}{y}^{(x - 4)}ln^{2}(y) - 6x{y}^{(x - 4)}ln^{2}(y) - 12{y}^{(x - 4)}ln(y) + \frac{96{x}^{(2y^{2} + 3)}}{x^{2}} + 22{y}^{(x - 4)} - 36x{y}^{(x - 4)} + 12x^{2}{y}^{(x - 4)}\right)}{dx}\\=&\frac{6240y^{2}*-2{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{6240y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{2}} + \frac{6240y^{2}{x}^{(2y^{2} + 3)}*2ln(x)}{x^{2}(x)} + \frac{7872y^{4}*-2{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{7872y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{2}} + \frac{7872y^{4}{x}^{(2y^{2} + 3)}*2ln(x)}{x^{2}(x)} + \frac{2688y^{2}*-2{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + \frac{2688y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln(x)}{x^{2}} + \frac{2688y^{2}{x}^{(2y^{2} + 3)}}{x^{2}(x)} + \frac{288*-2{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{288({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{2}} + \frac{288{x}^{(2y^{2} + 3)}*2ln(x)}{x^{2}(x)} + \frac{480*-2{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + \frac{480({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln(x)}{x^{2}} + \frac{480{x}^{(2y^{2} + 3)}}{x^{2}(x)} + 8*3x^{2}{y}^{(x - 4)}ln(y) + 8x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) + \frac{8x^{3}{y}^{(x - 4)}*0}{(y)} + \frac{8960y^{4}*-2{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{8960y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{2}} + \frac{8960y^{4}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{2}(x)} + \frac{5632y^{6}*-2{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{5632y^{6}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{2}} + \frac{5632y^{6}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{2}(x)} + \frac{2304y^{2}*-2{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{2304y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{2}} + \frac{2304y^{2}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{2}(x)} + \frac{2560y^{6}*-2{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{2560y^{6}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{2}} + \frac{2560y^{6}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{2}(x)} + \frac{1024y^{8}*-2{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{1024y^{8}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{2}} + \frac{1024y^{8}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{2}(x)} + \frac{1536y^{4}*-2{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{1536y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{2}} + \frac{1536y^{4}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{2}(x)} - 36*2x{y}^{(x - 4)}ln(y) - 36x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) - \frac{36x^{2}{y}^{(x - 4)}*0}{(y)} + 4x^{3}{y}^{(x - 4)}ln^{2}(y) + x^{4}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) + \frac{x^{4}{y}^{(x - 4)}*2ln(y)*0}{(y)} + 44{y}^{(x - 4)}ln(y) + 44x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) + \frac{44x{y}^{(x - 4)}*0}{(y)} - 6*3x^{2}{y}^{(x - 4)}ln^{2}(y) - 6x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) - \frac{6x^{3}{y}^{(x - 4)}*2ln(y)*0}{(y)} + 11*2x{y}^{(x - 4)}ln^{2}(y) + 11x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) + \frac{11x^{2}{y}^{(x - 4)}*2ln(y)*0}{(y)} - 6{y}^{(x - 4)}ln^{2}(y) - 6x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) - \frac{6x{y}^{(x - 4)}*2ln(y)*0}{(y)} - 12({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) - \frac{12{y}^{(x - 4)}*0}{(y)} + \frac{96*-2{x}^{(2y^{2} + 3)}}{x^{3}} + \frac{96({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))}{x^{2}} + 22({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) - 36{y}^{(x - 4)} - 36x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) + 12*2x{y}^{(x - 4)} + 12x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))\\=&\frac{13728y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{47232y^{4}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{16128y^{2}{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + \frac{32640y^{6}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{21120y^{4}{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + \frac{19712y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{288{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{1056{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + 36x^{2}{y}^{(x - 4)}ln(y) - 108x{y}^{(x - 4)}ln(y) + 12x^{3}{y}^{(x - 4)}ln^{2}(y) + \frac{33792y^{6}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{15360y^{8}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{2304y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{5632y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{6144y^{8}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{2048y^{10}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{1536y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} - 54x^{2}{y}^{(x - 4)}ln^{2}(y) + x^{4}{y}^{(x - 4)}ln^{3}(y) + 66{y}^{(x - 4)}ln(y) + 66x{y}^{(x - 4)}ln^{2}(y) - 6x^{3}{y}^{(x - 4)}ln^{3}(y) + 11x^{2}{y}^{(x - 4)}ln^{3}(y) - 6x{y}^{(x - 4)}ln^{3}(y) + \frac{2880y^{2}{x}^{(2y^{2} + 3)}}{x^{3}} - 18{y}^{(x - 4)}ln^{2}(y) + \frac{576{x}^{(2y^{2} + 3)}}{x^{3}} - 36{y}^{(x - 4)} + 24x{y}^{(x - 4)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{13728y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{47232y^{4}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{16128y^{2}{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + \frac{32640y^{6}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{21120y^{4}{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + \frac{19712y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{288{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{3}} + \frac{1056{x}^{(2y^{2} + 3)}ln(x)}{x^{3}} + 36x^{2}{y}^{(x - 4)}ln(y) - 108x{y}^{(x - 4)}ln(y) + 12x^{3}{y}^{(x - 4)}ln^{2}(y) + \frac{33792y^{6}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{15360y^{8}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{2304y^{2}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{3}} + \frac{5632y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{6144y^{8}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{2048y^{10}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} + \frac{1536y^{4}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{3}} - 54x^{2}{y}^{(x - 4)}ln^{2}(y) + x^{4}{y}^{(x - 4)}ln^{3}(y) + 66{y}^{(x - 4)}ln(y) + 66x{y}^{(x - 4)}ln^{2}(y) - 6x^{3}{y}^{(x - 4)}ln^{3}(y) + 11x^{2}{y}^{(x - 4)}ln^{3}(y) - 6x{y}^{(x - 4)}ln^{3}(y) + \frac{2880y^{2}{x}^{(2y^{2} + 3)}}{x^{3}} - 18{y}^{(x - 4)}ln^{2}(y) + \frac{576{x}^{(2y^{2} + 3)}}{x^{3}} - 36{y}^{(x - 4)} + 24x{y}^{(x - 4)}\right)}{dx}\\=&\frac{13728y^{2}*-3{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{13728y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{3}} + \frac{13728y^{2}{x}^{(2y^{2} + 3)}*2ln(x)}{x^{3}(x)} + \frac{47232y^{4}*-3{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{47232y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{3}} + \frac{47232y^{4}{x}^{(2y^{2} + 3)}*2ln(x)}{x^{3}(x)} + \frac{16128y^{2}*-3{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + \frac{16128y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln(x)}{x^{3}} + \frac{16128y^{2}{x}^{(2y^{2} + 3)}}{x^{3}(x)} + \frac{32640y^{6}*-3{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{32640y^{6}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{3}} + \frac{32640y^{6}{x}^{(2y^{2} + 3)}*2ln(x)}{x^{3}(x)} + \frac{21120y^{4}*-3{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + \frac{21120y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln(x)}{x^{3}} + \frac{21120y^{4}{x}^{(2y^{2} + 3)}}{x^{3}(x)} + \frac{19712y^{4}*-3{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{19712y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{3}} + \frac{19712y^{4}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{3}(x)} + \frac{288*-3{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{288({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{2}(x)}{x^{3}} + \frac{288{x}^{(2y^{2} + 3)}*2ln(x)}{x^{3}(x)} + \frac{1056*-3{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + \frac{1056({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln(x)}{x^{3}} + \frac{1056{x}^{(2y^{2} + 3)}}{x^{3}(x)} + 36*2x{y}^{(x - 4)}ln(y) + 36x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) + \frac{36x^{2}{y}^{(x - 4)}*0}{(y)} - 108{y}^{(x - 4)}ln(y) - 108x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) - \frac{108x{y}^{(x - 4)}*0}{(y)} + 12*3x^{2}{y}^{(x - 4)}ln^{2}(y) + 12x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) + \frac{12x^{3}{y}^{(x - 4)}*2ln(y)*0}{(y)} + \frac{33792y^{6}*-3{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{33792y^{6}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{3}} + \frac{33792y^{6}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{3}(x)} + \frac{15360y^{8}*-3{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{15360y^{8}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{3}} + \frac{15360y^{8}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{3}(x)} + \frac{2304y^{2}*-3{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{2304y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{3}(x)}{x^{3}} + \frac{2304y^{2}{x}^{(2y^{2} + 3)}*3ln^{2}(x)}{x^{3}(x)} + \frac{5632y^{6}*-3{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{5632y^{6}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{3}} + \frac{5632y^{6}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{3}(x)} + \frac{6144y^{8}*-3{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{6144y^{8}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{3}} + \frac{6144y^{8}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{3}(x)} + \frac{2048y^{10}*-3{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{2048y^{10}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{3}} + \frac{2048y^{10}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{3}(x)} + \frac{1536y^{4}*-3{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{1536y^{4}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))ln^{4}(x)}{x^{3}} + \frac{1536y^{4}{x}^{(2y^{2} + 3)}*4ln^{3}(x)}{x^{3}(x)} - 54*2x{y}^{(x - 4)}ln^{2}(y) - 54x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) - \frac{54x^{2}{y}^{(x - 4)}*2ln(y)*0}{(y)} + 4x^{3}{y}^{(x - 4)}ln^{3}(y) + x^{4}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{3}(y) + \frac{x^{4}{y}^{(x - 4)}*3ln^{2}(y)*0}{(y)} + 66({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln(y) + \frac{66{y}^{(x - 4)}*0}{(y)} + 66{y}^{(x - 4)}ln^{2}(y) + 66x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) + \frac{66x{y}^{(x - 4)}*2ln(y)*0}{(y)} - 6*3x^{2}{y}^{(x - 4)}ln^{3}(y) - 6x^{3}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{3}(y) - \frac{6x^{3}{y}^{(x - 4)}*3ln^{2}(y)*0}{(y)} + 11*2x{y}^{(x - 4)}ln^{3}(y) + 11x^{2}({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{3}(y) + \frac{11x^{2}{y}^{(x - 4)}*3ln^{2}(y)*0}{(y)} - 6{y}^{(x - 4)}ln^{3}(y) - 6x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{3}(y) - \frac{6x{y}^{(x - 4)}*3ln^{2}(y)*0}{(y)} + \frac{2880y^{2}*-3{x}^{(2y^{2} + 3)}}{x^{4}} + \frac{2880y^{2}({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))}{x^{3}} - 18({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))ln^{2}(y) - \frac{18{y}^{(x - 4)}*2ln(y)*0}{(y)} + \frac{576*-3{x}^{(2y^{2} + 3)}}{x^{4}} + \frac{576({x}^{(2y^{2} + 3)}((0 + 0)ln(x) + \frac{(2y^{2} + 3)(1)}{(x)}))}{x^{3}} - 36({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)})) + 24{y}^{(x - 4)} + 24x({y}^{(x - 4)}((1 + 0)ln(y) + \frac{(x - 4)(0)}{(y)}))\\=&\frac{7488y^{2}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{86592y^{4}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{29568y^{2}{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + \frac{195840y^{6}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{126720y^{4}{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + \frac{107520y^{6}{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + \frac{111360y^{8}{x}^{(2y^{2} + 3)}ln^{2}(x)}{x^{4}} + \frac{10752y^{4}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{61952y^{6}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{576{x}^{(2y^{2} + 3)}ln(x)}{x^{4}} + 96x{y}^{(x - 4)}ln(y) + 72x^{2}{y}^{(x - 4)}ln^{2}(y) - 144{y}^{(x - 4)}ln(y) - 216x{y}^{(x - 4)}ln^{2}(y) + \frac{92160y^{8}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + 16x^{3}{y}^{(x - 4)}ln^{3}(y) + \frac{3072y^{6}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{38912y^{10}{x}^{(2y^{2} + 3)}ln^{3}(x)}{x^{4}} + \frac{11264y^{8}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{12288y^{10}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} + \frac{4096y^{12}{x}^{(2y^{2} + 3)}ln^{4}(x)}{x^{4}} - 72x^{2}{y}^{(x - 4)}ln^{3}(y) + x^{4}{y}^{(x - 4)}ln^{4}(y) + 132{y}^{(x - 4)}ln^{2}(y) + 88x{y}^{(x - 4)}ln^{3}(y) - 6x^{3}{y}^{(x - 4)}ln^{4}(y) + \frac{17280y^{2}{x}^{(2y^{2} + 3)}}{x^{4}} + 11x^{2}{y}^{(x - 4)}ln^{4}(y) - 6x{y}^{(x - 4)}ln^{4}(y) - 24{y}^{(x - 4)}ln^{3}(y) + \frac{1056{x}^{(2y^{2} + 3)}}{x^{4}} + \frac{26880y^{4}{x}^{(2y^{2} + 3)}}{x^{4}} + 24{y}^{(x - 4)}\\ \end{split}\end{equation} \]

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