求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(\frac{(\frac{(\frac{ln(a)}{ln(b)})}{(\frac{ln(A)}{ln(c)})})}{(\frac{(\frac{ln(B)}{ln(d)})}{(\frac{ln(C)}{ln(D)})})})}{(\frac{(\frac{(\frac{ln(U)}{ln(V)})}{(\frac{ln(u)}{ln(W)})})}{(\frac{(\frac{ln(v)}{ln(X)})}{(\frac{ln(w)}{ln(x)})})})} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)}\right)}{dx}\\=&\frac{0ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{(a)ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)*-0ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{ln^{2}(b)(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)*-0ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{ln(b)ln^{2}(A)(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)*0ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)(c)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)*-0ln(d)ln(C)ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln^{2}(B)(B)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)*0ln(C)ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)(d)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)*0ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)(C)ln(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)ln^{2}(D)(D)ln(U)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)ln(D)ln^{2}(U)(U)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)*0ln(u)ln(v)ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)(V)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)ln(V)*0ln(v)ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)(u)ln(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)*-0ln(v)ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln^{2}(W)(W)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)*0ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)(v)ln(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln^{2}(X)(X)ln(w)} + \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(x)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln^{2}(w)(w)} + \frac{ln(a)ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)}{ln(b)ln(A)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)(x)}\\=&\frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{xln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{xln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\right)}{dx}\\=&\frac{-ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{0ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x(c)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)*-0ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{xln^{2}(B)(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)*0ln(C)ln(V)ln(u)ln(v)ln(a)}{xln(B)(d)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)*0ln(V)ln(u)ln(v)ln(a)}{xln(B)(C)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(a)}{xln(B)ln^{2}(D)(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(a)}{xln(B)ln(D)ln^{2}(U)(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)*0ln(u)ln(v)ln(a)}{xln(B)ln(D)ln(U)(V)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)*0ln(v)ln(a)}{xln(B)ln(D)ln(U)(u)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)*-0ln(v)ln(a)}{xln(B)ln(D)ln(U)ln^{2}(W)(W)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)*0ln(a)}{xln(B)ln(D)ln(U)ln(W)(v)ln(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(a)}{xln(B)ln(D)ln(U)ln(W)ln^{2}(X)(X)ln(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(a)}{xln(B)ln(D)ln(U)ln(W)ln(X)ln^{2}(w)(w)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*0}{xln(B)ln(D)ln(U)ln(W)ln(X)ln(w)(a)ln(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)*-0}{xln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln^{2}(b)(b)ln(A)} + \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)*-0}{xln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln^{2}(A)(A)}\\=&\frac{-ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\right)}{dx}\\=&\frac{--2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{0ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{2}(c)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)*-0ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{2}ln^{2}(B)(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)*0ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)(d)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)*0ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)(C)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)ln^{2}(D)(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(a)}{x^{2}ln(B)ln(D)ln^{2}(U)(U)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)*0ln(u)ln(v)ln(a)}{x^{2}ln(B)ln(D)ln(U)(V)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)*0ln(v)ln(a)}{x^{2}ln(B)ln(D)ln(U)(u)ln(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)*-0ln(v)ln(a)}{x^{2}ln(B)ln(D)ln(U)ln^{2}(W)(W)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)*0ln(a)}{x^{2}ln(B)ln(D)ln(U)ln(W)(v)ln(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(a)}{x^{2}ln(B)ln(D)ln(U)ln(W)ln^{2}(X)(X)ln(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(a)}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln^{2}(w)(w)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*0}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)(a)ln(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)*-0}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln^{2}(b)(b)ln(A)} - \frac{ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)*-0}{x^{2}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln^{2}(A)(A)}\\=&\frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\right)}{dx}\\=&\frac{2*-3ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{4}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2*0ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{3}(c)ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)*-0ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{3}ln^{2}(B)(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)*0ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)(d)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)*0ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)(C)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)ln^{2}(D)(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)*-0ln(V)ln(u)ln(v)ln(a)}{x^{3}ln(B)ln(D)ln^{2}(U)(U)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)*0ln(u)ln(v)ln(a)}{x^{3}ln(B)ln(D)ln(U)(V)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)*0ln(v)ln(a)}{x^{3}ln(B)ln(D)ln(U)(u)ln(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)*-0ln(v)ln(a)}{x^{3}ln(B)ln(D)ln(U)ln^{2}(W)(W)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)*0ln(a)}{x^{3}ln(B)ln(D)ln(U)ln(W)(v)ln(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(a)}{x^{3}ln(B)ln(D)ln(U)ln(W)ln^{2}(X)(X)ln(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*-0ln(a)}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln^{2}(w)(w)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)*0}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)(a)ln(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)*-0}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln^{2}(b)(b)ln(A)} + \frac{2ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)*-0}{x^{3}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln^{2}(A)(A)}\\=&\frac{-6ln(c)ln(d)ln(C)ln(V)ln(u)ln(v)ln(a)}{x^{4}ln(B)ln(D)ln(U)ln(W)ln(X)ln(w)ln(b)ln(A)}\\ \end{split}\end{equation} \]
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