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Derivada de la función/ xsqrt/ sqrt(x)/ xsqrt(x)arcctgx

Derivada de xsqrt(x)arcctgx

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

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Solución

Ha introducido [src] 
          2   
x*t*x*acot (x)
$$x t x \operatorname{acot}^{2}{\left(x \right)}$$ 
((x*t)*x)*acot(x)^2
Primera derivada [src] 
                            2        
    2                  2*t*x *acot(x)
acot (x)*(t*x + x*t) - --------------
                                2    
                           1 + x
$$- \frac{2 t x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \left(t x + t x\right) \operatorname{acot}^{2}{\left(x \right)}$$
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Segunda derivada [src] 
    /            2                                \
    |    2      x *(1 + 2*x*acot(x))   4*x*acot(x)|
2*t*|acot (x) + -------------------- - -----------|
    |                        2                 2  |
    |                /     2\             1 + x   |
    \                \1 + x /                     /
$$2 t \left(\frac{x^{2} \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \operatorname{acot}^{2}{\left(x \right)}\right)$$
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Tercera derivada [src] 
    /                /                       2        \                        \
    |              2 |            3*x     4*x *acot(x)|                        |
    |             x *|-acot(x) + ------ + ------------|                        |
    |                |                2           2   |                        |
    |                \           1 + x       1 + x    /   3*x*(1 + 2*x*acot(x))|
4*t*|-3*acot(x) - ------------------------------------- + ---------------------|
    |                                  2                               2       |
    \                             1 + x                           1 + x        /
--------------------------------------------------------------------------------
                                          2                                     
                                     1 + x
$$\frac{4 t \left(- \frac{x^{2} \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right)}{x^{2} + 1} + \frac{3 x \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{x^{2} + 1} - 3 \operatorname{acot}{\left(x \right)}\right)}{x^{2} + 1}$$
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