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4√2+arcctg^2x
The derivative of the function/ 4√2+arcctg^2x

Derivative of 4√2+arcctg^2x

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

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from to

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The solution

You have entered [src] 
    ___       2   
4*\/ 2  + acot (x)
acot⁡2(x)+42\operatorname{acot}^{2}{\left(x \right)} + 4 \sqrt{2} 
d /    ___       2   \
--\4*\/ 2  + acot (x)/
dx
ddx(acot⁡2(x)+42)\frac{d}{d x} \left(\operatorname{acot}^{2}{\left(x \right)} + 4 \sqrt{2}\right)
Transform
The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-2*acot(x)
----------
       2  
  1 + x
−2acot⁡(x)x2+1- \frac{2 \operatorname{acot}{\left(x \right)}}{x^{2} + 1}
Simplify
The second derivative [src] 
2*(1 + 2*x*acot(x))
-------------------
             2     
     /     2\      
     \1 + x /
2⋅(2xacot⁡(x)+1)(x2+1)2\frac{2 \cdot \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}
Simplify
The third derivative [src] 
  /              2                  \
  |   3*x     4*x *acot(x)          |
4*|- ------ - ------------ + acot(x)|
  |       2           2             |
  \  1 + x       1 + x              /
-------------------------------------
                      2              
              /     2\               
              \1 + x /
4(−4x2acot⁡(x)x2+1−3xx2+1+acot⁡(x))(x2+1)2\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}}
Simplify
The graph
Derivative of 4√2+arcctg^2x
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