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

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

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

Gráfico:

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Solución

Ha introducido [src] 
 5     2   
x *atan (x)
x5atan⁡2(x)x^{5} \operatorname{atan}^{2}{\left(x \right)} 
x^5*atan(x)^2
Gráfica
02468-8-6-4-2-1010-500000500000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                   5        
   4     2      2*x *atan(x)
5*x *atan (x) + ------------
                        2   
                   1 + x
2x5atan⁡(x)x2+1+5x4atan⁡2(x)\frac{2 x^{5} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 5 x^{4} \operatorname{atan}^{2}{\left(x \right)}
Simplificar
Segunda derivada [src] 
     /               2                                  \
   3 |       2      x *(-1 + 2*x*atan(x))   10*x*atan(x)|
2*x *|10*atan (x) - --------------------- + ------------|
     |                            2                 2   |
     |                    /     2\             1 + x    |
     \                    \1 + x /                      /
2x3(−x2(2xatan⁡(x)−1)(x2+1)2+10xatan⁡(x)x2+1+10atan⁡2(x))2 x^{3} \left(- \frac{x^{2} \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{10 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 10 \operatorname{atan}^{2}{\left(x \right)}\right)
Simplificar
Tercera derivada [src] 
     /                                              /            2                  \               \
     |                                            3 | 3*x     4*x *atan(x)          |               |
     |                                         2*x *|------ - ------------ + atan(x)|               |
     |                  2                           |     2           2             |               |
   2 |       2      15*x *(-1 + 2*x*atan(x))        \1 + x       1 + x              /   60*x*atan(x)|
2*x *|30*atan (x) - ------------------------ - -------------------------------------- + ------------|
     |                             2                                 2                          2   |
     |                     /     2\                          /     2\                      1 + x    |
     \                     \1 + x /                          \1 + x /                               /
2x2(−2x3(−4x2atan⁡(x)x2+1+3xx2+1+atan⁡(x))(x2+1)2−15x2(2xatan⁡(x)−1)(x2+1)2+60xatan⁡(x)x2+1+30atan⁡2(x))2 x^{2} \left(- \frac{2 x^{3} \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{15 x^{2} \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{60 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + 30 \operatorname{atan}^{2}{\left(x \right)}\right)
Simplificar
Gráfico
Derivada de y=x^5arctg^2*x
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