Mister Exam

Derivative of y=arctan(sinhx)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

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atan(sinh(x))
$$\operatorname{atan}{\left(\sinh{\left(x \right)} \right)}$$
d                
--(atan(sinh(x)))
dx               
$$\frac{d}{d x} \operatorname{atan}{\left(\sinh{\left(x \right)} \right)}$$
The graph
The first derivative [src]
  cosh(x)   
------------
        2   
1 + sinh (x)
$$\frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The second derivative [src]
/           2    \        
|     2*cosh (x) |        
|1 - ------------|*sinh(x)
|            2   |        
\    1 + sinh (x)/        
--------------------------
               2          
       1 + sinh (x)       
$$\frac{\left(- \frac{2 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} + 1\right) \sinh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The third derivative [src]
/           2              2             2        2   \        
|     6*sinh (x)     2*cosh (x)    8*cosh (x)*sinh (x)|        
|1 - ------------ - ------------ + -------------------|*cosh(x)
|            2              2                      2  |        
|    1 + sinh (x)   1 + sinh (x)     /        2   \   |        
\                                    \1 + sinh (x)/   /        
---------------------------------------------------------------
                                  2                            
                          1 + sinh (x)                         
$$\frac{\left(\frac{8 \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} - \frac{6 \sinh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} - \frac{2 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1} + 1\right) \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}$$
The graph
Derivative of y=arctan(sinhx)