Производная log(atan(sqrt(x)))

Вы ввели

   /    /  ___\\
log\atan\\/ x //

$$\log{\left (\operatorname{atan}{\left (\sqrt{x} \right )} \right )}$$

Первая производная

             1             
---------------------------
    ___             /  ___\
2*\/ x *(1 + x)*atan\\/ x /

$$\frac{1}{2 \sqrt{x} \left(x + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )}}$$

Вторая производная

 / 1           2                   1          \ 
-|---- + ------------- + ---------------------| 
 | 3/2     ___                         /  ___\| 
 \x      \/ x *(1 + x)   x*(1 + x)*atan\\/ x // 
------------------------------------------------
                           /  ___\              
             4*(1 + x)*atan\\/ x /              

$$- \frac{\frac{1}{x \left(x + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )}} + \frac{2}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}}{4 \left(x + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )}}$$

Третья производная

  3            1                1                       1                            3                          3            
------ + -------------- + -------------- + ---------------------------- + ------------------------ + ------------------------
   5/2     ___        2      3/2              3/2        2     2/  ___\              2     /  ___\      2             /  ___\
8*x      \/ x *(1 + x)    2*x   *(1 + x)   4*x   *(1 + x) *atan \\/ x /   4*x*(1 + x) *atan\\/ x /   8*x *(1 + x)*atan\\/ x /
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                                                                 /  ___\                                                     
                                                     (1 + x)*atan\\/ x /                                                     

$$\frac{1}{\left(x + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )}} \left(\frac{3}{4 x \left(x + 1\right)^{2} \operatorname{atan}{\left (\sqrt{x} \right )}} + \frac{3}{8 x^{2} \left(x + 1\right) \operatorname{atan}{\left (\sqrt{x} \right )}} + \frac{1}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{1}{2 x^{\frac{3}{2}} \left(x + 1\right)} + \frac{1}{4 x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left (\sqrt{x} \right )}} + \frac{3}{8 x^{\frac{5}{2}}}\right)$$