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x(ln^2)x+x^2arcctgx^6
Derivada de la función/ x+x^2/ x(ln^2)x/ x(ln^2)x+x^2arcctgx^6

Derivada de x(ln^2)x+x^2arcctgx^6

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     2         2     6   
x*log (x)*x + x *acot (x)
x2acot⁡6(x)+xxlog⁡(x)2x^{2} \operatorname{acot}^{6}{\left(x \right)} + x x \log{\left(x \right)}^{2} 
(x*log(x)^2)*x + x^2*acot(x)^6
Gráfica
02468-8-6-4-2-1010-5001000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                                       2     5   
     2        /   2              \           6      6*x *acot (x)
x*log (x) + x*\log (x) + 2*log(x)/ + 2*x*acot (x) - -------------
                                                             2   
                                                        1 + x
−6x2acot⁡5(x)x2+1+x(log⁡(x)2+2log⁡(x))+xlog⁡(x)2+2xacot⁡6(x)- \frac{6 x^{2} \operatorname{acot}^{5}{\left(x \right)}}{x^{2} + 1} + x \left(\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}\right) + x \log{\left(x \right)}^{2} + 2 x \operatorname{acot}^{6}{\left(x \right)}
Simplificar
Segunda derivada [src] 
  /                                             5         3     5          2     4   \
  |        6         2                 12*x*acot (x)   6*x *acot (x)   15*x *acot (x)|
2*|1 + acot (x) + log (x) + 3*log(x) - ------------- + ------------- + --------------|
  |                                             2                2               2   |
  |                                        1 + x         /     2\        /     2\    |
  \                                                      \1 + x /        \1 + x /    /
2(6x3acot⁡5(x)(x2+1)2+15x2acot⁡4(x)(x2+1)2−12xacot⁡5(x)x2+1+log⁡(x)2+3log⁡(x)+acot⁡6(x)+1)2 \left(\frac{6 x^{3} \operatorname{acot}^{5}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{15 x^{2} \operatorname{acot}^{4}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{12 x \operatorname{acot}^{5}{\left(x \right)}}{x^{2} + 1} + \log{\left(x \right)}^{2} + 3 \log{\left(x \right)} + \operatorname{acot}^{6}{\left(x \right)} + 1\right)
Simplificar
Tercera derivada [src] 
  /           5                     3     4          2     3          4     5          2     5               4   \
  |3   18*acot (x)   2*log(x)   90*x *acot (x)   60*x *acot (x)   24*x *acot (x)   42*x *acot (x)   90*x*acot (x)|
2*|- - ----------- + -------- - -------------- - -------------- - -------------- + -------------- + -------------|
  |x           2        x                 3                3                3                2                2  |
  |       1 + x                   /     2\         /     2\         /     2\         /     2\         /     2\   |
  \                               \1 + x /         \1 + x /         \1 + x /         \1 + x /         \1 + x /   /
2(−24x4acot⁡5(x)(x2+1)3−90x3acot⁡4(x)(x2+1)3+42x2acot⁡5(x)(x2+1)2−60x2acot⁡3(x)(x2+1)3+90xacot⁡4(x)(x2+1)2−18acot⁡5(x)x2+1+2log⁡(x)x+3x)2 \left(- \frac{24 x^{4} \operatorname{acot}^{5}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{90 x^{3} \operatorname{acot}^{4}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{42 x^{2} \operatorname{acot}^{5}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{60 x^{2} \operatorname{acot}^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{90 x \operatorname{acot}^{4}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{18 \operatorname{acot}^{5}{\left(x \right)}}{x^{2} + 1} + \frac{2 \log{\left(x \right)}}{x} + \frac{3}{x}\right)
Simplificar
Gráfico
Derivada de x(ln^2)x+x^2arcctgx^6
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