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y=(2x^2*sin(x)*tg(x^2+1))/sqrt(x^2+1)
Derivada de la función/ y=(2x^2*sin(x)*tg(x^2+1))/sqrt(x^2+1)

Derivada de y=(2x^2*sin(x)*tg(x^2+1))/sqrt(x^2+1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   2           / 2    \
2*x *sin(x)*tan\x  + 1/
-----------------------
         ________      
        /  2           
      \/  x  + 1
2x2sin⁡(x)tan⁡(x2+1)x2+1\frac{2 x^{2} \sin{\left(x \right)} \tan{\left(x^{2} + 1 \right)}}{\sqrt{x^{2} + 1}} 
(((2*x^2)*sin(x))*tan(x^2 + 1))/sqrt(x^2 + 1)
Gráfica
02468-8-6-4-2-1010-200000200000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/   2                    \    / 2    \      3 /       2/ 2    \\             3           / 2    \
\2*x *cos(x) + 4*x*sin(x)/*tan\x  + 1/ + 4*x *\1 + tan \x  + 1//*sin(x)   2*x *sin(x)*tan\x  + 1/
----------------------------------------------------------------------- - -----------------------
                                 ________                                               3/2      
                                /  2                                            / 2    \         
                              \/  x  + 1                                        \x  + 1/
−2x3sin⁡(x)tan⁡(x2+1)(x2+1)32+4x3(tan⁡2(x2+1)+1)sin⁡(x)+(2x2cos⁡(x)+4xsin⁡(x))tan⁡(x2+1)x2+1- \frac{2 x^{3} \sin{\left(x \right)} \tan{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{4 x^{3} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \sin{\left(x \right)} + \left(2 x^{2} \cos{\left(x \right)} + 4 x \sin{\left(x \right)}\right) \tan{\left(x^{2} + 1 \right)}}{\sqrt{x^{2} + 1}}
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Segunda derivada [src] 
  /                                                                                                                                                                                                                                                        /         2 \                   \
  |                                                                                                                                                                                                                                                      2 |      3*x  |           /     2\|
  |                                                                                                                                                                                                                                                     x *|-1 + ------|*sin(x)*tan\1 + x /|
  |                                                     2 /                         /     2\      2 /       2/     2\\       \                                                                                                                             |          2|                   |
  |/            2                    \    /     2\   2*x *\(2*sin(x) + x*cos(x))*tan\1 + x / + 2*x *\1 + tan \1 + x //*sin(x)/      2 /       2/     2\      2 /       2/     2\\    /     2\\             2 /       2/     2\\                            \     1 + x /                   |
2*|\2*sin(x) - x *sin(x) + 4*x*cos(x)/*tan\1 + x / - ------------------------------------------------------------------------- + 2*x *\1 + tan \1 + x / + 4*x *\1 + tan \1 + x //*tan\1 + x //*sin(x) + 4*x *\1 + tan \1 + x //*(2*sin(x) + x*cos(x)) + -----------------------------------|
  |                                                                                         2                                                                                                                                                                               2              |
  \                                                                                    1 + x                                                                                                                                                                           1 + x               /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                           ________                                                                                                                                         
                                                                                                                                          /      2                                                                                                                                          
                                                                                                                                        \/  1 + x
2(4x2(xcos⁡(x)+2sin⁡(x))(tan⁡2(x2+1)+1)+2x2(4x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+tan⁡2(x2+1)+1)sin⁡(x)+x2(3x2x2+1−1)sin⁡(x)tan⁡(x2+1)x2+1−2x2(2x2(tan⁡2(x2+1)+1)sin⁡(x)+(xcos⁡(x)+2sin⁡(x))tan⁡(x2+1))x2+1+(−x2sin⁡(x)+4xcos⁡(x)+2sin⁡(x))tan⁡(x2+1))x2+1\frac{2 \left(4 x^{2} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + 2 x^{2} \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + \tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \sin{\left(x \right)} + \frac{x^{2} \left(\frac{3 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(x \right)} \tan{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{2 x^{2} \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \sin{\left(x \right)} + \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \tan{\left(x^{2} + 1 \right)}\right)}{x^{2} + 1} + \left(- x^{2} \sin{\left(x \right)} + 4 x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \tan{\left(x^{2} + 1 \right)}\right)}{\sqrt{x^{2} + 1}}
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Tercera derivada [src] 
  /                                                                                                                                                                                                                                                                                                                                                                                          /         2 \                                                                                                                                                                            /         2 \                   \
  |                                                                                                                                                                                                                                                                                                                                                                                          |      3*x  | /                         /     2\      2 /       2/     2\\       \                                                                                                     3 |      5*x  |           /     2\|
  |                                                                                                                                                                                                                                                                                                                                                                                      3*x*|-1 + ------|*\(2*sin(x) + x*cos(x))*tan\1 + x / + 2*x *\1 + tan \1 + x //*sin(x)/                                                                                                  3*x *|-3 + ------|*sin(x)*tan\1 + x /|
  |                                                         //            2                    \    /     2\      2 /       2/     2\      2 /       2/     2\\    /     2\\             2 /       2/     2\\                      \                                                                                                                                                         |          2|                                                                                                                                                                            |          2|                   |
  |  /             2                    \    /     2\   3*x*\\2*sin(x) - x *sin(x) + 4*x*cos(x)/*tan\1 + x / + 2*x *\1 + tan \1 + x / + 4*x *\1 + tan \1 + x //*tan\1 + x //*sin(x) + 4*x *\1 + tan \1 + x //*(2*sin(x) + x*cos(x))/       /       2/     2\\ /            2                    \                             /       2/     2\      2 /       2/     2\\    /     2\\       \     1 + x /                                                                           3 /       2/     2\\ /     /     2\      2 /       2/     2\\      2    2/     2\\               \     1 + x /                   |
2*|- \-6*cos(x) + x *cos(x) + 6*x*sin(x)/*tan\1 + x / - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 6*x*\1 + tan \1 + x //*\2*sin(x) - x *sin(x) + 4*x*cos(x)/ + 6*x*(2*sin(x) + x*cos(x))*\1 + tan \1 + x / + 4*x *\1 + tan \1 + x //*tan\1 + x // + -------------------------------------------------------------------------------------- + 8*x *\1 + tan \1 + x //*\3*tan\1 + x / + 2*x *\1 + tan \1 + x // + 4*x *tan \1 + x //*sin(x) - -------------------------------------|
  |                                                                                                                                             2                                                                                                                                                                                                                                                                                     2                                                                                                                                                                2              |
  |                                                                                                                                        1 + x                                                                                                                                                                                                                                                                                 1 + x                                                                                                                                                         /     2\               |
  \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \1 + x /               /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                         ________                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                        /      2                                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                                      \/  1 + x
2(8x3(tan⁡2(x2+1)+1)(2x2(tan⁡2(x2+1)+1)+4x2tan⁡2(x2+1)+3tan⁡(x2+1))sin⁡(x)−3x3(5x2x2+1−3)sin⁡(x)tan⁡(x2+1)(x2+1)2+6x(xcos⁡(x)+2sin⁡(x))(4x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+tan⁡2(x2+1)+1)+6x(tan⁡2(x2+1)+1)(−x2sin⁡(x)+4xcos⁡(x)+2sin⁡(x))+3x(3x2x2+1−1)(2x2(tan⁡2(x2+1)+1)sin⁡(x)+(xcos⁡(x)+2sin⁡(x))tan⁡(x2+1))x2+1−3x(4x2(xcos⁡(x)+2sin⁡(x))(tan⁡2(x2+1)+1)+2x2(4x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+tan⁡2(x2+1)+1)sin⁡(x)+(−x2sin⁡(x)+4xcos⁡(x)+2sin⁡(x))tan⁡(x2+1))x2+1−(x2cos⁡(x)+6xsin⁡(x)−6cos⁡(x))tan⁡(x2+1))x2+1\frac{2 \left(8 x^{3} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + 4 x^{2} \tan^{2}{\left(x^{2} + 1 \right)} + 3 \tan{\left(x^{2} + 1 \right)}\right) \sin{\left(x \right)} - \frac{3 x^{3} \left(\frac{5 x^{2}}{x^{2} + 1} - 3\right) \sin{\left(x \right)} \tan{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2}} + 6 x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + \tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + 6 x \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \left(- x^{2} \sin{\left(x \right)} + 4 x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) + \frac{3 x \left(\frac{3 x^{2}}{x^{2} + 1} - 1\right) \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \sin{\left(x \right)} + \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \tan{\left(x^{2} + 1 \right)}\right)}{x^{2} + 1} - \frac{3 x \left(4 x^{2} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + 2 x^{2} \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + \tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \sin{\left(x \right)} + \left(- x^{2} \sin{\left(x \right)} + 4 x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \tan{\left(x^{2} + 1 \right)}\right)}{x^{2} + 1} - \left(x^{2} \cos{\left(x \right)} + 6 x \sin{\left(x \right)} - 6 \cos{\left(x \right)}\right) \tan{\left(x^{2} + 1 \right)}\right)}{\sqrt{x^{2} + 1}}
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Gráfico
Derivada de y=(2x^2*sin(x)*tg(x^2+1))/sqrt(x^2+1)
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