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y=5^x^2*arcctg*x^5
Derivada de la función/ y=5^x/ 5^x^2/ y=5^x^2*arcctg*x^5

Derivada de y=5^x^2*arcctg*x^5

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

Ha introducido [src] 
 / 2\         
 \x /     5   
5    *acot (x)
5x2acot⁡5(x)5^{x^{2}} \operatorname{acot}^{5}{\left(x \right)} 
5^(x^2)*acot(x)^5
Gráfica
02468-8-6-4-2-10105e66-3e66
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Primera derivada [src] 
     / 2\                                     
     \x /     4           / 2\                
  5*5    *acot (x)        \x /     5          
- ---------------- + 2*x*5    *acot (x)*log(5)
            2                                 
       1 + x
2⋅5x2xlog⁡(5)acot⁡5(x)−5⋅5x2acot⁡4(x)x2+12 \cdot 5^{x^{2}} x \log{\left(5 \right)} \operatorname{acot}^{5}{\left(x \right)} - \frac{5 \cdot 5^{x^{2}} \operatorname{acot}^{4}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
   / 2\                                                                                       
   \x /     3    /5*(2 + x*acot(x))       2    /       2       \          10*x*acot(x)*log(5)\
2*5    *acot (x)*|----------------- + acot (x)*\1 + 2*x *log(5)/*log(5) - -------------------|
                 |            2                                                       2      |
                 |    /     2\                                                   1 + x       |
                 \    \1 + x /                                                               /
2⋅5x2(−10xlog⁡(5)acot⁡(x)x2+1+(2x2log⁡(5)+1)log⁡(5)acot⁡2(x)+5(xacot⁡(x)+2)(x2+1)2)acot⁡3(x)2 \cdot 5^{x^{2}} \left(- \frac{10 x \log{\left(5 \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \left(2 x^{2} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \operatorname{acot}^{2}{\left(x \right)} + \frac{5 \left(x \operatorname{acot}{\left(x \right)} + 2\right)}{\left(x^{2} + 1\right)^{2}}\right) \operatorname{acot}^{3}{\left(x \right)}
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Tercera derivada [src] 
                 /    /                         2     2                  \                                                                                                                      \
                 |    |      2        6      4*x *acot (x)   12*x*acot(x)|                                                                                                                      |
                 |  5*|- acot (x) + ------ + ------------- + ------------|                                                                                                                      |
   / 2\          |    |                  2            2              2   |          2    /       2       \                                                                                      |
   \x /     2    |    \             1 + x        1 + x          1 + x    /   15*acot (x)*\1 + 2*x *log(5)/*log(5)           3       2    /       2       \   30*x*(2 + x*acot(x))*acot(x)*log(5)|
2*5    *acot (x)*|- ------------------------------------------------------ - ------------------------------------ + 2*x*acot (x)*log (5)*\3 + 2*x *log(5)/ + -----------------------------------|
                 |                                2                                              2                                                                                2             |
                 |                        /     2\                                          1 + x                                                                         /     2\              |
                 \                        \1 + x /                                                                                                                        \1 + x /              /
2⋅5x2(2x(2x2log⁡(5)+3)log⁡(5)2acot⁡3(x)+30x(xacot⁡(x)+2)log⁡(5)acot⁡(x)(x2+1)2−15(2x2log⁡(5)+1)log⁡(5)acot⁡2(x)x2+1−5(4x2acot⁡2(x)x2+1+12xacot⁡(x)x2+1−acot⁡2(x)+6x2+1)(x2+1)2)acot⁡2(x)2 \cdot 5^{x^{2}} \left(2 x \left(2 x^{2} \log{\left(5 \right)} + 3\right) \log{\left(5 \right)}^{2} \operatorname{acot}^{3}{\left(x \right)} + \frac{30 x \left(x \operatorname{acot}{\left(x \right)} + 2\right) \log{\left(5 \right)} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{15 \left(2 x^{2} \log{\left(5 \right)} + 1\right) \log{\left(5 \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{5 \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{12 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{6}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}}\right) \operatorname{acot}^{2}{\left(x \right)}
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Gráfico
Derivada de y=5^x^2*arcctg*x^5
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