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y=arctg(x/2)−ln√4(x^4-16)
Derivada de la función/ (x/2)/ x^4-1/ arctg/ y=arctg(x/2)−ln√4(x^4-16)

Derivada de y=arctg(x/2)−ln√4(x^4-16)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
             /         0.25\
    /x\      |/ 4     \    |
atan|-| - log\\x  - 16/    /
    \2/
−log⁡((x4−16)0.25)+atan⁡(x2)- \log{\left(\left(x^{4} - 16\right)^{0.25} \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
atan(x/2) - log((x^4 - 16)^0.25)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                             -1.0
    1             3 / 4     \    
---------- - 1.0*x *\x  - 16/    
  /     2\                       
  |    x |                       
2*|1 + --|                       
  \    4 /
−1.0x3(x4−16)1.0+12(x24+1)- \frac{1.0 x^{3}}{\left(x^{4} - 16\right)^{1.0}} + \frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}
Simplificar
Segunda derivada [src] 
  /                                -2.0                    -1.0\
  |      16            5 /       4\              /       4\    |
x*|- --------- + 16.0*x *\-16 + x /     - 12.0*x*\-16 + x /    |
  |          2                                                 |
  |  /     2\                                                  |
  \  \4 + x /                                                  /
----------------------------------------------------------------
                               4
x(16.0x5(x4−16)2.0−12.0x(x4−16)1.0−16(x2+4)2)4\frac{x \left(\frac{16.0 x^{5}}{\left(x^{4} - 16\right)^{2.0}} - \frac{12.0 x}{\left(x^{4} - 16\right)^{1.0}} - \frac{16}{\left(x^{2} + 4\right)^{2}}\right)}{4}
Simplificar
Tercera derivada [src] 
                    2                       -2.0                     -3.0                   -1.0
      4         16*x            5 /       4\             9 /       4\             /       4\    
- --------- + --------- + 36.0*x *\-16 + x /     - 32.0*x *\-16 + x /     - 6.0*x*\-16 + x /    
          2           3                                                                         
  /     2\    /     2\                                                                          
  \4 + x /    \4 + x /
−32.0x9(x4−16)3.0+36.0x5(x4−16)2.0+16x2(x2+4)3−6.0x(x4−16)1.0−4(x2+4)2- \frac{32.0 x^{9}}{\left(x^{4} - 16\right)^{3.0}} + \frac{36.0 x^{5}}{\left(x^{4} - 16\right)^{2.0}} + \frac{16 x^{2}}{\left(x^{2} + 4\right)^{3}} - \frac{6.0 x}{\left(x^{4} - 16\right)^{1.0}} - \frac{4}{\left(x^{2} + 4\right)^{2}}
Simplificar
Gráfico
Derivada de y=arctg(x/2)−ln√4(x^4-16)
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