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y=5*((x^2)+(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))*ctg(8x)^3

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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= cinco *((x^ dos)+(x)^(uno / dos)+ uno /x)^(uno / dos)-e^(cos(tres x))*ctg(8x)^3
  • y es igual a 5 multiplicar por ((x al cuadrado ) más (x) en el grado (1 dividir por 2) más 1 dividir por x) en el grado (1 dividir por 2) menos e en el grado ( coseno de (3x)) multiplicar por ctg(8x) al cubo
  • y es igual a cinco multiplicar por ((x en el grado dos) más (x) en el grado (uno dividir por dos) más uno dividir por x) en el grado (uno dividir por dos) menos e en el grado ( coseno de (tres x)) multiplicar por ctg(8x) al cubo
  • y=5*((x2)+(x)(1/2)+1/x)(1/2)-e(cos(3x))*ctg(8x)3
  • y=5*x2+x1/2+1/x1/2-ecos3x*ctg8x3
  • y=5*((x²)+(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))*ctg(8x)³
  • y=5*((x en el grado 2)+(x) en el grado (1/2)+1/x) en el grado (1/2)-e en el grado (cos(3x))*ctg(8x) en el grado 3
  • y=5((x^2)+(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))ctg(8x)^3
  • y=5((x2)+(x)(1/2)+1/x)(1/2)-e(cos(3x))ctg(8x)3
  • y=5x2+x1/2+1/x1/2-ecos3xctg8x3
  • y=5x^2+x^1/2+1/x^1/2-e^cos3xctg8x^3
  • y=5*((x^2)+(x)^(1 dividir por 2)+1 dividir por x)^(1 dividir por 2)-e^(cos(3x))*ctg(8x)^3

  • Expresiones semejantes

  • y=5*((x^2)+(x)^(1/2)-1/x)^(1/2)-e^(cos(3x))*ctg(8x)^3
  • y=5*((x^2)-(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))*ctg(8x)^3
  • y=5*((x^2)+(x)^(1/2)+1/x)^(1/2)+e^(cos(3x))*ctg(8x)^3
Derivada de la función/ y=5*((x^2)+(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))*ctg(8x)^3

Derivada de y=5*((x^2)+(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))*ctg(8x)^3

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
      ________________                      
     /  2     ___   1     cos(3*x)    3     
5*  /  x  + \/ x  + -  - E        *cot (8*x)
  \/                x
−ecos⁡(3x)cot⁡3(8x)+5(x+x2)+1x- e^{\cos{\left(3 x \right)}} \cot^{3}{\left(8 x \right)} + 5 \sqrt{\left(\sqrt{x} + x^{2}\right) + \frac{1}{x}} 
5*sqrt(x^2 + sqrt(x) + 1/x) - E^cos(3*x)*cot(8*x)^3
Gráfica
02468-8-6-4-2-1010-50000000005000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
  /     1        1   \                                                                            
5*|x - ---- + -------|                                                                            
  |       2       ___|                                                                            
  \    2*x    4*\/ x /      2      /            2     \  cos(3*x)        3       cos(3*x)         
---------------------- - cot (8*x)*\-24 - 24*cot (8*x)/*e         + 3*cot (8*x)*e        *sin(3*x)
     ________________                                                                             
    /  2     ___   1                                                                              
   /  x  + \/ x  + -                                                                              
 \/                x
−(−24cot⁡2(8x)−24)ecos⁡(3x)cot⁡2(8x)+3ecos⁡(3x)sin⁡(3x)cot⁡3(8x)+5(x−12x2+14x)(x+x2)+1x- \left(- 24 \cot^{2}{\left(8 x \right)} - 24\right) e^{\cos{\left(3 x \right)}} \cot^{2}{\left(8 x \right)} + 3 e^{\cos{\left(3 x \right)}} \sin{\left(3 x \right)} \cot^{3}{\left(8 x \right)} + \frac{5 \left(x - \frac{1}{2 x^{2}} + \frac{1}{4 \sqrt{x}}\right)}{\sqrt{\left(\sqrt{x} + x^{2}\right) + \frac{1}{x}}}
Simplificar
Segunda derivada [src] 
                      2                                                                                                                                                                                                                                    
    /  1     2       \         /     1     8 \                                                                                                                                                                                                             
  5*|----- - -- + 4*x|       5*|8 - ---- + --|                                                                                                                                                                                                             
    |  ___    2      |         |     3/2    3|                         2                                                                                                                                                                                   
    \\/ x    x       /         \    x      x /          /       2     \            cos(3*x)          3      /       2     \  cos(3*x)        3         2       cos(3*x)        3                cos(3*x)          2      /       2     \  cos(3*x)         
- ---------------------- + ---------------------- - 384*\1 + cot (8*x)/ *cot(8*x)*e         - 384*cot (8*x)*\1 + cot (8*x)/*e         - 9*cot (8*x)*sin (3*x)*e         + 9*cot (8*x)*cos(3*x)*e         - 144*cot (8*x)*\1 + cot (8*x)/*e        *sin(3*x)
                     3/2         ________________                                                                                                                                                                                                          
     /  ___   1    2\           /   ___   1    2                                                                                                                                                                                                           
  16*|\/ x  + - + x |      8*  /  \/ x  + - + x                                                                                                                                                                                                            
     \        x     /        \/           x
−384(cot⁡2(8x)+1)2ecos⁡(3x)cot⁡(8x)−144(cot⁡2(8x)+1)ecos⁡(3x)sin⁡(3x)cot⁡2(8x)−384(cot⁡2(8x)+1)ecos⁡(3x)cot⁡3(8x)+5(8+8x3−1x32)8x+x2+1x−9ecos⁡(3x)sin⁡2(3x)cot⁡3(8x)+9ecos⁡(3x)cos⁡(3x)cot⁡3(8x)−5(4x−2x2+1x)216(x+x2+1x)32- 384 \left(\cot^{2}{\left(8 x \right)} + 1\right)^{2} e^{\cos{\left(3 x \right)}} \cot{\left(8 x \right)} - 144 \left(\cot^{2}{\left(8 x \right)} + 1\right) e^{\cos{\left(3 x \right)}} \sin{\left(3 x \right)} \cot^{2}{\left(8 x \right)} - 384 \left(\cot^{2}{\left(8 x \right)} + 1\right) e^{\cos{\left(3 x \right)}} \cot^{3}{\left(8 x \right)} + \frac{5 \left(8 + \frac{8}{x^{3}} - \frac{1}{x^{\frac{3}{2}}}\right)}{8 \sqrt{\sqrt{x} + x^{2} + \frac{1}{x}}} - 9 e^{\cos{\left(3 x \right)}} \sin^{2}{\left(3 x \right)} \cot^{3}{\left(8 x \right)} + 9 e^{\cos{\left(3 x \right)}} \cos{\left(3 x \right)} \cot^{3}{\left(8 x \right)} - \frac{5 \left(4 x - \frac{2}{x^{2}} + \frac{1}{\sqrt{x}}\right)^{2}}{16 \left(\sqrt{x} + x^{2} + \frac{1}{x}\right)^{\frac{3}{2}}}
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Tercera derivada [src] 
  /                                                                                3                                                                                                                                                                                                                                                                                                                                                                                                                                                            \
  |                                        /   1     16\         /  1     2       \                                                                                                                                                                 /     1     8 \ /  1     2       \                                                                                                                                                                                                                                                          |
  |                                      5*|- ---- + --|       5*|----- - -- + 4*x|                                                                                                                                                               5*|8 - ---- + --|*|----- - -- + 4*x|                                                                                                                                                                                                                                                          |
  |                    3                   |   5/2    4|         |  ___    2      |                                                                                                                                       2                         |     3/2    3| |  ___    2      |                                                                                                                                                                         2                                                                                |
  |     /       2     \   cos(3*x)         \  x      x /         \\/ x    x       /          3       cos(3*x)                 3         3       cos(3*x)           4      /       2     \  cos(3*x)        /       2     \     2       cos(3*x)     \    x      x / \\/ x    x       /          2      /       2     \           cos(3*x)         3                cos(3*x)                   2         2      /       2     \  cos(3*x)        /       2     \            cos(3*x)                    3      /       2     \  cos(3*x)         |
3*|1024*\1 + cot (8*x)/ *e         - ----------------------- + ---------------------- - 9*cot (8*x)*e        *sin(3*x) + 9*cot (8*x)*sin (3*x)*e         + 2048*cot (8*x)*\1 + cot (8*x)/*e         + 7168*\1 + cot (8*x)/ *cot (8*x)*e         - ------------------------------------ - 216*cot (8*x)*\1 + cot (8*x)/*cos(3*x)*e         - 27*cot (8*x)*cos(3*x)*e        *sin(3*x) + 216*cot (8*x)*sin (3*x)*\1 + cot (8*x)/*e         + 1152*\1 + cot (8*x)/ *cot(8*x)*e        *sin(3*x) + 1152*cot (8*x)*\1 + cot (8*x)/*e        *sin(3*x)|
  |                                         ________________                      5/2                                                                                                                                                                                       3/2                                                                                                                                                                                                                                                                 |
  |                                        /   ___   1    2       /  ___   1    2\                                                                                                                                                                          /  ___   1    2\                                                                                                                                                                                                                                                                    |
  |                                  16*  /  \/ x  + - + x     64*|\/ x  + - + x |                                                                                                                                                                       32*|\/ x  + - + x |                                                                                                                                                                                                                                                                    |
  \                                     \/           x            \        x     /                                                                                                                                                                          \        x     /                                                                                                                                                                                                                                                                    /
3(−5(16x4−1x52)16x+x2+1x+1024(cot⁡2(8x)+1)3ecos⁡(3x)+1152(cot⁡2(8x)+1)2ecos⁡(3x)sin⁡(3x)cot⁡(8x)+7168(cot⁡2(8x)+1)2ecos⁡(3x)cot⁡2(8x)+216(cot⁡2(8x)+1)ecos⁡(3x)sin⁡2(3x)cot⁡2(8x)+1152(cot⁡2(8x)+1)ecos⁡(3x)sin⁡(3x)cot⁡3(8x)−216(cot⁡2(8x)+1)ecos⁡(3x)cos⁡(3x)cot⁡2(8x)+2048(cot⁡2(8x)+1)ecos⁡(3x)cot⁡4(8x)−5(8+8x3−1x32)(4x−2x2+1x)32(x+x2+1x)32+9ecos⁡(3x)sin⁡3(3x)cot⁡3(8x)−27ecos⁡(3x)sin⁡(3x)cos⁡(3x)cot⁡3(8x)−9ecos⁡(3x)sin⁡(3x)cot⁡3(8x)+5(4x−2x2+1x)364(x+x2+1x)52)3 \left(- \frac{5 \left(\frac{16}{x^{4}} - \frac{1}{x^{\frac{5}{2}}}\right)}{16 \sqrt{\sqrt{x} + x^{2} + \frac{1}{x}}} + 1024 \left(\cot^{2}{\left(8 x \right)} + 1\right)^{3} e^{\cos{\left(3 x \right)}} + 1152 \left(\cot^{2}{\left(8 x \right)} + 1\right)^{2} e^{\cos{\left(3 x \right)}} \sin{\left(3 x \right)} \cot{\left(8 x \right)} + 7168 \left(\cot^{2}{\left(8 x \right)} + 1\right)^{2} e^{\cos{\left(3 x \right)}} \cot^{2}{\left(8 x \right)} + 216 \left(\cot^{2}{\left(8 x \right)} + 1\right) e^{\cos{\left(3 x \right)}} \sin^{2}{\left(3 x \right)} \cot^{2}{\left(8 x \right)} + 1152 \left(\cot^{2}{\left(8 x \right)} + 1\right) e^{\cos{\left(3 x \right)}} \sin{\left(3 x \right)} \cot^{3}{\left(8 x \right)} - 216 \left(\cot^{2}{\left(8 x \right)} + 1\right) e^{\cos{\left(3 x \right)}} \cos{\left(3 x \right)} \cot^{2}{\left(8 x \right)} + 2048 \left(\cot^{2}{\left(8 x \right)} + 1\right) e^{\cos{\left(3 x \right)}} \cot^{4}{\left(8 x \right)} - \frac{5 \left(8 + \frac{8}{x^{3}} - \frac{1}{x^{\frac{3}{2}}}\right) \left(4 x - \frac{2}{x^{2}} + \frac{1}{\sqrt{x}}\right)}{32 \left(\sqrt{x} + x^{2} + \frac{1}{x}\right)^{\frac{3}{2}}} + 9 e^{\cos{\left(3 x \right)}} \sin^{3}{\left(3 x \right)} \cot^{3}{\left(8 x \right)} - 27 e^{\cos{\left(3 x \right)}} \sin{\left(3 x \right)} \cos{\left(3 x \right)} \cot^{3}{\left(8 x \right)} - 9 e^{\cos{\left(3 x \right)}} \sin{\left(3 x \right)} \cot^{3}{\left(8 x \right)} + \frac{5 \left(4 x - \frac{2}{x^{2}} + \frac{1}{\sqrt{x}}\right)^{3}}{64 \left(\sqrt{x} + x^{2} + \frac{1}{x}\right)^{\frac{5}{2}}}\right)
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Gráfico
Derivada de y=5*((x^2)+(x)^(1/2)+1/x)^(1/2)-e^(cos(3x))*ctg(8x)^3
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