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y=arctg²(x+√1+x²)
Derivada de la función/ arctg/ y=arctg²(x+√1+x²)

Derivada de y=arctg²(x+√1+x²)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    2/      ___    2\
atan \x + \/ 1  + x /
atan⁡2(x2+(x+1))\operatorname{atan}^{2}{\left(x^{2} + \left(x + \sqrt{1}\right) \right)} 
atan(x + sqrt(1) + x^2)^2
Gráfica
02468-8-6-4-2-10105-5
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Primera derivada [src] 
                /      ___    2\
2*(1 + 2*x)*atan\x + \/ 1  + x /
--------------------------------
                         2      
         /      ___    2\       
     1 + \x + \/ 1  + x /
2(2x+1)atan⁡(x2+(x+1))(x2+(x+1))2+1\frac{2 \left(2 x + 1\right) \operatorname{atan}{\left(x^{2} + \left(x + \sqrt{1}\right) \right)}}{\left(x^{2} + \left(x + \sqrt{1}\right)\right)^{2} + 1}
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Segunda derivada [src] 
  /                                  2                 2 /         2\     /         2\\
  |      /         2\       (1 + 2*x)       2*(1 + 2*x) *\1 + x + x /*atan\1 + x + x /|
2*|2*atan\1 + x + x / + ----------------- - ------------------------------------------|
  |                                     2                               2             |
  |                         /         2\                    /         2\              |
  \                     1 + \1 + x + x /                1 + \1 + x + x /              /
---------------------------------------------------------------------------------------
                                                   2                                   
                                       /         2\                                    
                                   1 + \1 + x + x /
2(−2(2x+1)2(x2+x+1)atan⁡(x2+x+1)(x2+x+1)2+1+(2x+1)2(x2+x+1)2+1+2atan⁡(x2+x+1))(x2+x+1)2+1\frac{2 \left(- \frac{2 \left(2 x + 1\right)^{2} \left(x^{2} + x + 1\right) \operatorname{atan}{\left(x^{2} + x + 1 \right)}}{\left(x^{2} + x + 1\right)^{2} + 1} + \frac{\left(2 x + 1\right)^{2}}{\left(x^{2} + x + 1\right)^{2} + 1} + 2 \operatorname{atan}{\left(x^{2} + x + 1 \right)}\right)}{\left(x^{2} + x + 1\right)^{2} + 1}
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Tercera derivada [src] 
            /                                                                                                                         2                 \
            |                                                                               2 /         2\              2 /         2\      /         2\|
            |             2     /         2\     /         2\     /         2\   3*(1 + 2*x) *\1 + x + x /   4*(1 + 2*x) *\1 + x + x / *atan\1 + x + x /|
4*(1 + 2*x)*|3 - (1 + 2*x) *atan\1 + x + x / - 6*\1 + x + x /*atan\1 + x + x / - ------------------------- + -------------------------------------------|
            |                                                                                        2                                    2             |
            |                                                                            /         2\                         /         2\              |
            \                                                                        1 + \1 + x + x /                     1 + \1 + x + x /              /
---------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                      2                                                                  
                                                                   /                2\                                                                   
                                                                   |    /         2\ |                                                                   
                                                                   \1 + \1 + x + x / /
4(2x+1)(−(2x+1)2atan⁡(x2+x+1)+4(2x+1)2(x2+x+1)2atan⁡(x2+x+1)(x2+x+1)2+1−3(2x+1)2(x2+x+1)(x2+x+1)2+1−6(x2+x+1)atan⁡(x2+x+1)+3)((x2+x+1)2+1)2\frac{4 \left(2 x + 1\right) \left(- \left(2 x + 1\right)^{2} \operatorname{atan}{\left(x^{2} + x + 1 \right)} + \frac{4 \left(2 x + 1\right)^{2} \left(x^{2} + x + 1\right)^{2} \operatorname{atan}{\left(x^{2} + x + 1 \right)}}{\left(x^{2} + x + 1\right)^{2} + 1} - \frac{3 \left(2 x + 1\right)^{2} \left(x^{2} + x + 1\right)}{\left(x^{2} + x + 1\right)^{2} + 1} - 6 \left(x^{2} + x + 1\right) \operatorname{atan}{\left(x^{2} + x + 1 \right)} + 3\right)}{\left(\left(x^{2} + x + 1\right)^{2} + 1\right)^{2}}
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Gráfico
Derivada de y=arctg²(x+√1+x²)
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