Mister Exam

Other calculators


4√2+arcctg^2x

Derivative of 4√2+arcctg^2x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    ___       2   
4*\/ 2  + acot (x)
$$\operatorname{acot}^{2}{\left(x \right)} + 4 \sqrt{2}$$
d /    ___       2   \
--\4*\/ 2  + acot (x)/
dx                    
$$\frac{d}{d x} \left(\operatorname{acot}^{2}{\left(x \right)} + 4 \sqrt{2}\right)$$
The graph
The first derivative [src]
-2*acot(x)
----------
       2  
  1 + x   
$$- \frac{2 \operatorname{acot}{\left(x \right)}}{x^{2} + 1}$$
The second derivative [src]
2*(1 + 2*x*acot(x))
-------------------
             2     
     /     2\      
     \1 + x /      
$$\frac{2 \cdot \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}$$
The third derivative [src]
  /              2                  \
  |   3*x     4*x *acot(x)          |
4*|- ------ - ------------ + acot(x)|
  |       2           2             |
  \  1 + x       1 + x              /
-------------------------------------
                      2              
              /     2\               
              \1 + x /               
$$\frac{4 \left(- \frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \frac{3 x}{x^{2} + 1} + \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}$$
The graph
Derivative of 4√2+arcctg^2x