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y=4x^3-2arctg^5*(2*x^5-6)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de 4*y Derivada de 4*y
  • Derivada de -1/y Derivada de -1/y
  • Derivada de (14-x)*e^14-x Derivada de (14-x)*e^14-x
  • Derivada de -17x^2 Derivada de -17x^2

  • Expresiones idénticas

  • y=4x^ tres - dos arctg^ cinco *(2*x^ cinco - seis)
  • y es igual a 4x al cubo menos 2arctg en el grado 5 multiplicar por (2 multiplicar por x en el grado 5 menos 6)
  • y es igual a 4x en el grado tres menos dos arctg en el grado cinco multiplicar por (2 multiplicar por x en el grado cinco menos seis)
  • y=4x3-2arctg5*(2*x5-6)
  • y=4x3-2arctg5*2*x5-6
  • y=4x³-2arctg⁵*(2*x⁵-6)
  • y=4x en el grado 3-2arctg en el grado 5*(2*x en el grado 5-6)
  • y=4x^3-2arctg^5(2x^5-6)
  • y=4x3-2arctg5(2x5-6)
  • y=4x3-2arctg52x5-6
  • y=4x^3-2arctg^52x^5-6

  • Expresiones semejantes

  • y=4x^3-2arctg^5*(2*x^5+6)
  • y=4x^3+2arctg^5*(2*x^5-6)
Derivada de la función/ arctg/ x^3-2/ y=4x^3/ 2*x^5/ y=4x^3-2arctg^5*(2*x^5-6)

Derivada de y=4x^3-2arctg^5*(2*x^5-6)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   3         5/   5    \
4*x  - 2*atan \2*x  - 6/
4x3−2atan⁡5(2x5−6)4 x^{3} - 2 \operatorname{atan}^{5}{\left(2 x^{5} - 6 \right)} 
4*x^3 - 2*atan(2*x^5 - 6)^5
Gráfica
02468-8-6-4-2-1010-1000010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
             4     4/   5    \
    2   100*x *atan \2*x  - 6/
12*x  - ----------------------
                         2    
               /   5    \     
           1 + \2*x  - 6/
−100x4atan⁡4(2x5−6)(2x5−6)2+1+12x2- \frac{100 x^{4} \operatorname{atan}^{4}{\left(2 x^{5} - 6 \right)}}{\left(2 x^{5} - 6\right)^{2} + 1} + 12 x^{2}
Simplificar
Segunda derivada [src] 
    /         7     3/  /      5\\       2     4/  /      5\\        7     4/  /      5\\ /      5\\
    |    500*x *atan \2*\-3 + x //   50*x *atan \2*\-3 + x //   500*x *atan \2*\-3 + x //*\-3 + x /|
8*x*|3 - ------------------------- - ------------------------ + -----------------------------------|
    |                         2                         2                                 2        |
    |       /               2\                 /      5\                /               2\         |
    |       |      /      5\ |           1 + 4*\-3 + x /                |      /      5\ |         |
    \       \1 + 4*\-3 + x / /                                          \1 + 4*\-3 + x / /         /
8x(500x7(x5−3)atan⁡4(2(x5−3))(4(x5−3)2+1)2−500x7atan⁡3(2(x5−3))(4(x5−3)2+1)2−50x2atan⁡4(2(x5−3))4(x5−3)2+1+3)8 x \left(\frac{500 x^{7} \left(x^{5} - 3\right) \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{500 x^{7} \operatorname{atan}^{3}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{50 x^{2} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{4 \left(x^{5} - 3\right)^{2} + 1} + 3\right)
Simplificar
Tercera derivada [src] 
  /                                                                                                                                             2                                                                                                   \
  |           12     2/  /      5\\         7     3/  /      5\\        2     4/  /      5\\         12     4/  /      5\\          12 /      5\      4/  /      5\\         7     4/  /      5\\ /      5\          12     3/  /      5\\ /      5\|
  |    15000*x  *atan \2*\-3 + x //   6000*x *atan \2*\-3 + x //   150*x *atan \2*\-3 + x //   2500*x  *atan \2*\-3 + x //   40000*x  *\-3 + x / *atan \2*\-3 + x //   6000*x *atan \2*\-3 + x //*\-3 + x /   60000*x  *atan \2*\-3 + x //*\-3 + x /|
8*|3 - ---------------------------- - -------------------------- - ------------------------- + --------------------------- - --------------------------------------- + ------------------------------------ + --------------------------------------|
  |                          3                             2                           2                             2                                   3                                       2                                       3          |
  |        /               2\            /               2\                   /      5\            /               2\                  /               2\                      /               2\                      /               2\           |
  |        |      /      5\ |            |      /      5\ |             1 + 4*\-3 + x /            |      /      5\ |                  |      /      5\ |                      |      /      5\ |                      |      /      5\ |           |
  \        \1 + 4*\-3 + x / /            \1 + 4*\-3 + x / /                                        \1 + 4*\-3 + x / /                  \1 + 4*\-3 + x / /                      \1 + 4*\-3 + x / /                      \1 + 4*\-3 + x / /           /
8(−40000x12(x5−3)2atan⁡4(2(x5−3))(4(x5−3)2+1)3+60000x12(x5−3)atan⁡3(2(x5−3))(4(x5−3)2+1)3+2500x12atan⁡4(2(x5−3))(4(x5−3)2+1)2−15000x12atan⁡2(2(x5−3))(4(x5−3)2+1)3+6000x7(x5−3)atan⁡4(2(x5−3))(4(x5−3)2+1)2−6000x7atan⁡3(2(x5−3))(4(x5−3)2+1)2−150x2atan⁡4(2(x5−3))4(x5−3)2+1+3)8 \left(- \frac{40000 x^{12} \left(x^{5} - 3\right)^{2} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{3}} + \frac{60000 x^{12} \left(x^{5} - 3\right) \operatorname{atan}^{3}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{3}} + \frac{2500 x^{12} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{15000 x^{12} \operatorname{atan}^{2}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{3}} + \frac{6000 x^{7} \left(x^{5} - 3\right) \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{6000 x^{7} \operatorname{atan}^{3}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{150 x^{2} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{4 \left(x^{5} - 3\right)^{2} + 1} + 3\right)
Simplificar
3-я производная [src] 
  /                                                                                                                                             2                                                                                                   \
  |           12     2/  /      5\\         7     3/  /      5\\        2     4/  /      5\\         12     4/  /      5\\          12 /      5\      4/  /      5\\         7     4/  /      5\\ /      5\          12     3/  /      5\\ /      5\|
  |    15000*x  *atan \2*\-3 + x //   6000*x *atan \2*\-3 + x //   150*x *atan \2*\-3 + x //   2500*x  *atan \2*\-3 + x //   40000*x  *\-3 + x / *atan \2*\-3 + x //   6000*x *atan \2*\-3 + x //*\-3 + x /   60000*x  *atan \2*\-3 + x //*\-3 + x /|
8*|3 - ---------------------------- - -------------------------- - ------------------------- + --------------------------- - --------------------------------------- + ------------------------------------ + --------------------------------------|
  |                          3                             2                           2                             2                                   3                                       2                                       3          |
  |        /               2\            /               2\                   /      5\            /               2\                  /               2\                      /               2\                      /               2\           |
  |        |      /      5\ |            |      /      5\ |             1 + 4*\-3 + x /            |      /      5\ |                  |      /      5\ |                      |      /      5\ |                      |      /      5\ |           |
  \        \1 + 4*\-3 + x / /            \1 + 4*\-3 + x / /                                        \1 + 4*\-3 + x / /                  \1 + 4*\-3 + x / /                      \1 + 4*\-3 + x / /                      \1 + 4*\-3 + x / /           /
8(−40000x12(x5−3)2atan⁡4(2(x5−3))(4(x5−3)2+1)3+60000x12(x5−3)atan⁡3(2(x5−3))(4(x5−3)2+1)3+2500x12atan⁡4(2(x5−3))(4(x5−3)2+1)2−15000x12atan⁡2(2(x5−3))(4(x5−3)2+1)3+6000x7(x5−3)atan⁡4(2(x5−3))(4(x5−3)2+1)2−6000x7atan⁡3(2(x5−3))(4(x5−3)2+1)2−150x2atan⁡4(2(x5−3))4(x5−3)2+1+3)8 \left(- \frac{40000 x^{12} \left(x^{5} - 3\right)^{2} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{3}} + \frac{60000 x^{12} \left(x^{5} - 3\right) \operatorname{atan}^{3}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{3}} + \frac{2500 x^{12} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{15000 x^{12} \operatorname{atan}^{2}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{3}} + \frac{6000 x^{7} \left(x^{5} - 3\right) \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{6000 x^{7} \operatorname{atan}^{3}{\left(2 \left(x^{5} - 3\right) \right)}}{\left(4 \left(x^{5} - 3\right)^{2} + 1\right)^{2}} - \frac{150 x^{2} \operatorname{atan}^{4}{\left(2 \left(x^{5} - 3\right) \right)}}{4 \left(x^{5} - 3\right)^{2} + 1} + 3\right)
Simplificar
Gráfico
Derivada de y=4x^3-2arctg^5*(2*x^5-6)
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