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y=arctg^2(sqrt(x))
Derivada de la función/ sqrt(x)/ ctg^2/ arctg/ y=arctg^2(sqrt(x))

Derivada de y=arctg^2(sqrt(x))

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

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Solución

Ha introducido [src] 
    2/  ___\
atan \\/ x /
atan⁡2(x)\operatorname{atan}^{2}{\left(\sqrt{x} \right)} 
atan(sqrt(x))^2
Gráfica
02468-8-6-4-2-1010-2525
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Primera derivada [src] 
     /  ___\ 
 atan\\/ x / 
-------------
  ___        
\/ x *(1 + x)
atan⁡(x)x(x+1)\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(x + 1\right)}
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Segunda derivada [src] 
                  /  ___\        /  ___\ 
     1        atan\\/ x /    atan\\/ x / 
----------- - ----------- - -------------
2*x*(1 + x)         3/2       ___        
                 2*x        \/ x *(1 + x)
-----------------------------------------
                  1 + x
12x(x+1)−atan⁡(x)x(x+1)−atan⁡(x)2x32x+1\frac{\frac{1}{2 x \left(x + 1\right)} - \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(x + 1\right)} - \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}}}}{x + 1}
Simplificar
3-я производная [src] 
                                      /  ___\       /  ___\          /  ___\ 
       3              3         3*atan\\/ x /   atan\\/ x /    2*atan\\/ x / 
- ------------ - ------------ + ------------- + ------------ + --------------
             2      2                  5/2       3/2             ___        2
  2*x*(1 + x)    4*x *(1 + x)       4*x         x   *(1 + x)   \/ x *(1 + x) 
-----------------------------------------------------------------------------
                                    1 + x
−32x(x+1)2−34x2(x+1)+2atan⁡(x)x(x+1)2+atan⁡(x)x32(x+1)+3atan⁡(x)4x52x+1\frac{- \frac{3}{2 x \left(x + 1\right)^{2}} - \frac{3}{4 x^{2} \left(x + 1\right)} + \frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(x + 1\right)} + \frac{3 \operatorname{atan}{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}}}}{x + 1}
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Tercera derivada [src] 
                                      /  ___\       /  ___\          /  ___\ 
       3              3         3*atan\\/ x /   atan\\/ x /    2*atan\\/ x / 
- ------------ - ------------ + ------------- + ------------ + --------------
             2      2                  5/2       3/2             ___        2
  2*x*(1 + x)    4*x *(1 + x)       4*x         x   *(1 + x)   \/ x *(1 + x) 
-----------------------------------------------------------------------------
                                    1 + x
−32x(x+1)2−34x2(x+1)+2atan⁡(x)x(x+1)2+atan⁡(x)x32(x+1)+3atan⁡(x)4x52x+1\frac{- \frac{3}{2 x \left(x + 1\right)^{2}} - \frac{3}{4 x^{2} \left(x + 1\right)} + \frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(x + 1\right)} + \frac{3 \operatorname{atan}{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}}}}{x + 1}
Simplificar
Gráfico
Derivada de y=arctg^2(sqrt(x))
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