Mister Exam

Other calculators

arctg(shx)+(shx)×lnchx
The derivative of the function/ arctg(shx)+(shx)×lnchx

Derivative of arctg(shx)+(shx)×lnchx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
atan(sinh(x)) + sinh(x)*log(cosh(x))
log⁡(cosh⁡(x))sinh⁡(x)+atan⁡(sinh⁡(x))\log{\left(\cosh{\left(x \right)} \right)} \sinh{\left(x \right)} + \operatorname{atan}{\left(\sinh{\left(x \right)} \right)} 
d                                       
--(atan(sinh(x)) + sinh(x)*log(cosh(x)))
dx
ddx(log⁡(cosh⁡(x))sinh⁡(x)+atan⁡(sinh⁡(x)))\frac{d}{d x} \left(\log{\left(\cosh{\left(x \right)} \right)} \sinh{\left(x \right)} + \operatorname{atan}{\left(\sinh{\left(x \right)} \right)}\right)
Transform
The graph
02468-8-6-4-2-1010-200000200000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                   2                          
  cosh(x)      sinh (x)                       
------------ + -------- + cosh(x)*log(cosh(x))
        2      cosh(x)                        
1 + sinh (x)
log⁡(cosh⁡(x))cosh⁡(x)+sinh⁡2(x)cosh⁡(x)+cosh⁡(x)sinh⁡2(x)+1\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}
Simplify
The second derivative [src] 
/                       2               2                    \        
|         1         sinh (x)      2*cosh (x)                 |        
|3 + ------------ - -------- - --------------- + log(cosh(x))|*sinh(x)
|            2          2                    2               |        
|    1 + sinh (x)   cosh (x)   /        2   \                |        
\                              \1 + sinh (x)/                /
(log⁡(cosh⁡(x))−sinh⁡2(x)cosh⁡2(x)+3−2cosh⁡2(x)(sinh⁡2(x)+1)2+1sinh⁡2(x)+1)sinh⁡(x)\left(\log{\left(\cosh{\left(x \right)} \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + 3 - \frac{2 \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} + \frac{1}{\sinh^{2}{\left(x \right)} + 1}\right) \sinh{\left(x \right)}
Simplify
The third derivative [src] 
                                                           3              2            4            2                    3        2   
              cosh(x)                                2*cosh (x)     2*sinh (x)   2*sinh (x)   6*sinh (x)*cosh(x)   8*cosh (x)*sinh (x)
3*cosh(x) + ------------ + cosh(x)*log(cosh(x)) - --------------- - ---------- + ---------- - ------------------ + -------------------
                    2                                           2    cosh(x)          3                      2                     3  
            1 + sinh (x)                          /        2   \                  cosh (x)     /        2   \        /        2   \   
                                                  \1 + sinh (x)/                               \1 + sinh (x)/        \1 + sinh (x)/
log⁡(cosh⁡(x))cosh⁡(x)+8sinh⁡2(x)cosh⁡3(x)(sinh⁡2(x)+1)3+2sinh⁡4(x)cosh⁡3(x)−2sinh⁡2(x)cosh⁡(x)+3cosh⁡(x)−6sinh⁡2(x)cosh⁡(x)(sinh⁡2(x)+1)2−2cosh⁡3(x)(sinh⁡2(x)+1)2+cosh⁡(x)sinh⁡2(x)+1\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{8 \sinh^{2}{\left(x \right)} \cosh^{3}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{3}} + \frac{2 \sinh^{4}{\left(x \right)}}{\cosh^{3}{\left(x \right)}} - \frac{2 \sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + 3 \cosh{\left(x \right)} - \frac{6 \sinh^{2}{\left(x \right)} \cosh{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} - \frac{2 \cosh^{3}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + 1\right)^{2}} + \frac{\cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + 1}
Simplify
The graph
Derivative of arctg(shx)+(shx)×lnchx
    © Mister Exam – Calculator