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Derivada de la función/ sqrt(x)/ arctg/ а^(arctgsqrt(x))

Derivada de а^(arctgsqrt(x))

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

Ha introducido [src] 
     /  ___\
 atan\\/ x /
a
$$a^{\operatorname{atan}{\left(\sqrt{x} \right)}}$$ 
a^atan(sqrt(x))
Primera derivada [src] 
     /  ___\       
 atan\\/ x /       
a           *log(a)
-------------------
      ___          
  2*\/ x *(1 + x)
$$\frac{a^{\operatorname{atan}{\left(\sqrt{x} \right)}} \log{\left(a \right)}}{2 \sqrt{x} \left(x + 1\right)}$$
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Segunda derivada [src] 
     /  ___\                                            
 atan\\/ x / /   1           2           log(a) \       
a           *|- ---- - ------------- + ---------|*log(a)
             |   3/2     ___           x*(1 + x)|       
             \  x      \/ x *(1 + x)            /       
--------------------------------------------------------
                       4*(1 + x)
$$\frac{a^{\operatorname{atan}{\left(\sqrt{x} \right)}} \left(\frac{\log{\left(a \right)}}{x \left(x + 1\right)} - \frac{2}{\sqrt{x} \left(x + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(a \right)}}{4 \left(x + 1\right)}$$
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Tercera derivada [src] 
     /  ___\ /                                                                                2       \       
 atan\\/ x / |  3            1                1            3*log(a)       3*log(a)         log (a)    |       
a           *|------ + -------------- + -------------- - ------------ - ------------ + ---------------|*log(a)
             |   5/2     ___        2      3/2                      2      2              3/2        2|       
             \8*x      \/ x *(1 + x)    2*x   *(1 + x)   4*x*(1 + x)    8*x *(1 + x)   8*x   *(1 + x) /       
--------------------------------------------------------------------------------------------------------------
                                                    1 + x
$$\frac{a^{\operatorname{atan}{\left(\sqrt{x} \right)}} \left(- \frac{3 \log{\left(a \right)}}{4 x \left(x + 1\right)^{2}} - \frac{3 \log{\left(a \right)}}{8 x^{2} \left(x + 1\right)} + \frac{1}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{1}{2 x^{\frac{3}{2}} \left(x + 1\right)} + \frac{\log{\left(a \right)}^{2}}{8 x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3}{8 x^{\frac{5}{2}}}\right) \log{\left(a \right)}}{x + 1}$$
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