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y=5^arctg^2√x
Derivada de la función/ ctg^2/ arctg/ y=5^arctg^2√x

Derivada de y=5^arctg^2√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 /
5
5atan⁡2(x)5^{\operatorname{atan}^{2}{\left(\sqrt{x} \right)}} 
5^(atan(sqrt(x))^2)
Gráfica
02468-8-6-4-2-1010020
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Primera derivada [src] 
     2/  ___\                   
 atan \\/ x /     /  ___\       
5            *atan\\/ x /*log(5)
--------------------------------
           ___                  
         \/ x *(1 + x)
5atan⁡2(x)log⁡(5)atan⁡(x)x(x+1)\frac{5^{\operatorname{atan}^{2}{\left(\sqrt{x} \right)}} \log{\left(5 \right)} \operatorname{atan}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(x + 1\right)}
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Segunda derivada [src] 
     2/  ___\ /                  /  ___\        /  ___\        2/  ___\       \       
 atan \\/ x / |     1        atan\\/ x /    atan\\/ x /    atan \\/ x /*log(5)|       
5            *|----------- - ----------- - ------------- + -------------------|*log(5)
              |2*x*(1 + x)         3/2       ___                x*(1 + x)     |       
              \                 2*x        \/ x *(1 + x)                      /       
--------------------------------------------------------------------------------------
                                        1 + x
5atan⁡2(x)(log⁡(5)atan⁡2(x)x(x+1)+12x(x+1)−atan⁡(x)x(x+1)−atan⁡(x)2x32)log⁡(5)x+1\frac{5^{\operatorname{atan}^{2}{\left(\sqrt{x} \right)}} \left(\frac{\log{\left(5 \right)} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}}{x \left(x + 1\right)} + \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}}}\right) \log{\left(5 \right)}}{x + 1}
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Tercera derivada [src] 
     2/  ___\ /                                      /  ___\       /  ___\          /  ___\        3/  ___\    2            2/  ___\                2/  ___\                /  ___\       \       
 atan \\/ x / |       3              3         3*atan\\/ x /   atan\\/ x /    2*atan\\/ x /    atan \\/ x /*log (5)   3*atan \\/ x /*log(5)   3*atan \\/ x /*log(5)   3*atan\\/ x /*log(5)|       
5            *|- ------------ - ------------ + ------------- + ------------ + -------------- + -------------------- - --------------------- - --------------------- + --------------------|*log(5)
              |             2      2                  5/2       3/2             ___        2       3/2        2                      2                2                    3/2        2   |       
              \  2*x*(1 + x)    4*x *(1 + x)       4*x         x   *(1 + x)   \/ x *(1 + x)       x   *(1 + x)              x*(1 + x)              2*x *(1 + x)         2*x   *(1 + x)    /       
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                              1 + x
5atan⁡2(x)(−3log⁡(5)atan⁡2(x)x(x+1)2−32x(x+1)2−3log⁡(5)atan⁡2(x)2x2(x+1)−34x2(x+1)+2atan⁡(x)x(x+1)2+atan⁡(x)x32(x+1)+log⁡(5)2atan⁡3(x)x32(x+1)2+3log⁡(5)atan⁡(x)2x32(x+1)2+3atan⁡(x)4x52)log⁡(5)x+1\frac{5^{\operatorname{atan}^{2}{\left(\sqrt{x} \right)}} \left(- \frac{3 \log{\left(5 \right)} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}}{x \left(x + 1\right)^{2}} - \frac{3}{2 x \left(x + 1\right)^{2}} - \frac{3 \log{\left(5 \right)} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}}{2 x^{2} \left(x + 1\right)} - \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{\log{\left(5 \right)}^{2} \operatorname{atan}^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3 \log{\left(5 \right)} \operatorname{atan}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3 \operatorname{atan}{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}}}\right) \log{\left(5 \right)}}{x + 1}
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Gráfico
Derivada de y=5^arctg^2√x
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