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  • Derivada de:
  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)
  • Derivada de u/v

  • Expresiones idénticas

  • y=arctg^ tres *ln*sqrtx/x+ dos
  • y es igual a arctg al cubo multiplicar por ln multiplicar por raíz cuadrada de x dividir por x más 2
  • y es igual a arctg en el grado tres multiplicar por ln multiplicar por raíz cuadrada de x dividir por x más dos
  • y=arctg^3*ln*√x/x+2
  • y=arctg3*ln*sqrtx/x+2
  • y=arctg³*ln*sqrtx/x+2
  • y=arctg en el grado 3*ln*sqrtx/x+2
  • y=arctg^3lnsqrtx/x+2
  • y=arctg3lnsqrtx/x+2
  • y=arctg^3*ln*sqrtx dividir por x+2

  • Expresiones semejantes

  • y=arctg^3*ln*sqrtx/x-2
Derivada de la función/ x/x+2/ arctg/ sqrtx/ y=arctg^3*ln*sqrtx/x+2

Derivada de y=arctg^3*ln*sqrtx/x+2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    3       / 2\        
atan (x)*log\x /*t*x    
-------------------- + 2
         x
2+xtlog⁡(x2)atan⁡3(x)x2 + \frac{x t \log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x} 
(((atan(x)^3*log(x^2))*t)*x)/x + 2
Primera derivada [src] 
                         /      3            2       / 2\\                     
    3       / 2\         |2*atan (x)   3*atan (x)*log\x /|                     
atan (x)*log\x /*t + t*x*|---------- + ------------------|                     
                         |    x                   2      |         3       / 2\
                         \                   1 + x       /   t*atan (x)*log\x /
---------------------------------------------------------- - ------------------
                            x                                        x
−tlog⁡(x2)atan⁡3(x)x+tx(3log⁡(x2)atan⁡2(x)x2+1+2atan⁡3(x)x)+tlog⁡(x2)atan⁡3(x)x- \frac{t \log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x} + \frac{t x \left(\frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{x}\right) + t \log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x}
Simplificar
Segunda derivada [src] 
  /                                                                                                                                      /  /                 / 2\\                  \                            \        
  |                                                                                                                                      |  |2*atan(x)   3*log\x /|              / 2\|                            |        
  |                                                                                                                                      |x*|--------- + ---------| + atan(x)*log\x /|*atan(x)                    |        
  |      /    2           / 2\                               / 2\\         2        /                 / 2\\               2       / 2\   |  |    x              2 |                  |                        / 2\|        
  |      |atan (x)   3*log\x /   6*atan(x)    3*x*atan(x)*log\x /|   2*atan (x)     |2*atan(x)   3*log\x /|           atan (x)*log\x /   \  \              1 + x  /                  /           3*atan(x)*log\x /|        
t*|- 2*x*|-------- - --------- - ---------- + -------------------| - ---------- + 2*|--------- + ---------|*atan(x) + ---------------- - ----------------------------------------------------- - -----------------|*atan(x)
  |      |    2              2     /     2\                2     |       x          |    x              2 |                  x                                     x                                        2     |        
  |      |   x       /     2\    x*\1 + x /        /     2\      |                  \              1 + x  /                                                                                            1 + x      |        
  \      \           \1 + x /                      \1 + x /      /                                                                                                                                                /        
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                             x
t(−2x(3xlog⁡(x2)atan⁡(x)(x2+1)2−3log⁡(x2)(x2+1)2−6atan⁡(x)x(x2+1)+atan⁡2(x)x2)+2(3log⁡(x2)x2+1+2atan⁡(x)x)atan⁡(x)−3log⁡(x2)atan⁡(x)x2+1−(x(3log⁡(x2)x2+1+2atan⁡(x)x)+log⁡(x2)atan⁡(x))atan⁡(x)x+log⁡(x2)atan⁡2(x)x−2atan⁡2(x)x)atan⁡(x)x\frac{t \left(- 2 x \left(\frac{3 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) + 2 \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)} - \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{\left(x \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) + \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}}{x} + \frac{\log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{x} - \frac{2 \operatorname{atan}^{2}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)}}{x}
Simplificar
Tercera derivada [src] 
    /  /         2            3           / 2\          2            2       / 2\                                 / 2\       2     2       / 2\\     /    2           / 2\                               / 2\\                                                                                                                    /  /    2           / 2\                               / 2\\   /                 / 2\\        \                                                                      \
    |  |  18*atan (x)   2*atan (x)   3*log\x /    9*atan (x)   3*atan (x)*log\x /    18*atan(x)   18*x*atan(x)*log\x /   12*x *atan (x)*log\x /|     |atan (x)   3*log\x /   6*atan(x)    3*x*atan(x)*log\x /|                                 /  /                 / 2\\                  \                                      |  |atan (x)   3*log\x /   6*atan(x)    3*x*atan(x)*log\x /|   |2*atan(x)   3*log\x /|        |                                                                      |
    |x*|- ----------- + ---------- + --------- - ----------- - ------------------ + ----------- - -------------------- + ----------------------| - 3*|-------- - --------- - ---------- + -------------------|*atan(x)                    2    |  |2*atan(x)   3*log\x /|              / 2\|                                    2*|x*|-------- - --------- - ---------- + -------------------| - |--------- + ---------|*atan(x)|*atan(x)                                                              |
    |  |           2         3               3    2 /     2\               2                  2                3                       3       |     |    2              2     /     2\                2     |                        atan (x)*|x*|--------- + ---------| + atan(x)*log\x /|                                      |  |    2              2     /     2\                2     |   |    x              2 |        |                                                                      |
    |  |   /     2\         x        /     2\    x *\1 + x /       /     2\           /     2\         /     2\                /     2\        |     |   x       /     2\    x*\1 + x /        /     2\      |                 3               |  |    x              2 |                  |       3       / 2\          2        |  |   x       /     2\    x*\1 + x /        /     2\      |   \              1 + x  /        |                 2       / 2\                / 2\         2       / 2\|
    |  \   \1 + x /                  \1 + x /                      \1 + x /         x*\1 + x /         \1 + x /                \1 + x /        /     \           \1 + x /                      \1 + x /      /           3*atan (x)            \  \              1 + x  /                  /   atan (x)*log\x /    6*atan (x)     \  \           \1 + x /                      \1 + x /      /                                  /           3*atan (x)*log\x /   3*atan(x)*log\x /   3*atan (x)*log\x /|
2*t*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------- + ------------------------------------------------------ - ---------------- - ----------- + --------------------------------------------------------------------------------------------------------- + ------------------ - ----------------- + ------------------|
    |                                                                                                        x                                                                                                                3                                  3                                     3           2 /     2\                                                        2                                                                  2                     2          2 /     2\    |
    |                                                                                                                                                                                                                        x                                  x                                     x           x *\1 + x /                                                       x                                                           /     2\              /     2\          x *\1 + x /    |
    \                                                                                                                                                                                                                                                                                                                                                                                                                                           \1 + x /            x*\1 + x /                         /
2t(3log⁡(x2)atan⁡2(x)(x2+1)2+x(12x2log⁡(x2)atan⁡2(x)(x2+1)3−18xlog⁡(x2)atan⁡(x)(x2+1)3−3log⁡(x2)atan⁡2(x)(x2+1)2−18atan⁡2(x)(x2+1)2+3log⁡(x2)(x2+1)3+18atan⁡(x)x(x2+1)2−9atan⁡2(x)x2(x2+1)+2atan⁡3(x)x3)−3(3xlog⁡(x2)atan⁡(x)(x2+1)2−3log⁡(x2)(x2+1)2−6atan⁡(x)x(x2+1)+atan⁡2(x)x2)atan⁡(x)x−3log⁡(x2)atan⁡(x)x(x2+1)2+2(x(3xlog⁡(x2)atan⁡(x)(x2+1)2−3log⁡(x2)(x2+1)2−6atan⁡(x)x(x2+1)+atan⁡2(x)x2)−(3log⁡(x2)x2+1+2atan⁡(x)x)atan⁡(x))atan⁡(x)x2+3log⁡(x2)atan⁡2(x)x2(x2+1)−6atan⁡2(x)x2(x2+1)+(x(3log⁡(x2)x2+1+2atan⁡(x)x)+log⁡(x2)atan⁡(x))atan⁡2(x)x3−log⁡(x2)atan⁡3(x)x3+3atan⁡3(x)x3)2 t \left(\frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{x \left(\frac{12 x^{2} \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{18 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{18 \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{18 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2}} - \frac{9 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{x^{3}}\right) - 3 \left(\frac{3 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x \right)}}{x} - \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2}} + \frac{2 \left(x \left(\frac{3 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) - \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}}{x^{2}} + \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} - \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{\left(x \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) + \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{3}} - \frac{\log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x^{3}} + \frac{3 \operatorname{atan}^{3}{\left(x \right)}}{x^{3}}\right)
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