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1/4(arctg(2x)^4)
The derivative of the function/ 1/4(arctg(2x)^4)

Derivative of 1/4(arctg(2x)^4)

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] 
    4     
atan (2*x)
----------
    4
atan⁡4(2x)4\frac{\operatorname{atan}^{4}{\left(2 x \right)}}{4} 
  /    4     \
d |atan (2*x)|
--|----------|
dx\    4     /
ddxatan⁡4(2x)4\frac{d}{d x} \frac{\operatorname{atan}^{4}{\left(2 x \right)}}{4}
Transform
The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      3     
2*atan (2*x)
------------
         2  
  1 + 4*x
2atan⁡3(2x)4x2+1\frac{2 \operatorname{atan}^{3}{\left(2 x \right)}}{4 x^{2} + 1}
Simplify
The second derivative [src] 
       2                          
-4*atan (2*x)*(-3 + 4*x*atan(2*x))
----------------------------------
                     2            
           /       2\             
           \1 + 4*x /
−4⋅(4xatan⁡(2x)−3)atan⁡2(2x)(4x2+1)2- \frac{4 \cdot \left(4 x \operatorname{atan}{\left(2 x \right)} - 3\right) \operatorname{atan}^{2}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}}
Simplify
The third derivative [src] 
   /                                               2     2     \          
   |      2           3       18*x*atan(2*x)   16*x *atan (2*x)|          
16*|- atan (2*x) + -------- - -------------- + ----------------|*atan(2*x)
   |                      2             2                 2    |          
   \               1 + 4*x       1 + 4*x           1 + 4*x     /          
--------------------------------------------------------------------------
                                         2                                
                               /       2\                                 
                               \1 + 4*x /
16⋅(16x2atan⁡2(2x)4x2+1−atan⁡2(2x)−18xatan⁡(2x)4x2+1+34x2+1)atan⁡(2x)(4x2+1)2\frac{16 \cdot \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} - \frac{18 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{3}{4 x^{2} + 1}\right) \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}}
Simplify
The graph
Derivative of 1/4(arctg(2x)^4)
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