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(x^2+1)^sin(2*x)
Derivada de la función/ x^2+1/ sin(2*x)/ (x^2+1)^sin(2*x)

Derivada de (x^2+1)^sin(2*x)

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

Ha introducido [src] 
        sin(2*x)
/ 2    \        
\x  + 1/
(x2+1)sin⁡(2x)\left(x^{2} + 1\right)^{\sin{\left(2 x \right)}} 
(x^2 + 1)^sin(2*x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(sin⁡(2x))+1)sin⁡sin⁡(2x)(2x)\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}

Respuesta:

(log⁡(sin⁡(2x))+1)sin⁡sin⁡(2x)(2x)\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}

Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        sin(2*x)                                        
/ 2    \         /              / 2    \   2*x*sin(2*x)\
\x  + 1/        *|2*cos(2*x)*log\x  + 1/ + ------------|
                 |                             2       |
                 \                            x  + 1   /
(x2+1)sin⁡(2x)(2xsin⁡(2x)x2+1+2log⁡(x2+1)cos⁡(2x))\left(x^{2} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{2 x \sin{\left(2 x \right)}}{x^{2} + 1} + 2 \log{\left(x^{2} + 1 \right)} \cos{\left(2 x \right)}\right)
Simplificar
Segunda derivada [src] 
          sin(2*x) /                                     2                                          2                        \
  /     2\         |  /            /     2\   x*sin(2*x)\    sin(2*x)        /     2\            2*x *sin(2*x)   4*x*cos(2*x)|
2*\1 + x /        *|2*|cos(2*x)*log\1 + x / + ----------|  + -------- - 2*log\1 + x /*sin(2*x) - ------------- + ------------|
                   |  |                              2  |          2                                       2             2   |
                   |  \                         1 + x   /     1 + x                                /     2\         1 + x    |
                   \                                                                               \1 + x /                  /
2(x2+1)sin⁡(2x)(−2x2sin⁡(2x)(x2+1)2+4xcos⁡(2x)x2+1+2(xsin⁡(2x)x2+1+log⁡(x2+1)cos⁡(2x))2−2log⁡(x2+1)sin⁡(2x)+sin⁡(2x)x2+1)2 \left(x^{2} + 1\right)^{\sin{\left(2 x \right)}} \left(- \frac{2 x^{2} \sin{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4 x \cos{\left(2 x \right)}}{x^{2} + 1} + 2 \left(\frac{x \sin{\left(2 x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(2 x \right)}\right)^{2} - 2 \log{\left(x^{2} + 1 \right)} \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{2} + 1}\right)
Simplificar
Tercera derivada [src] 
          sin(2*x) /                                     3                                         /                                                        2         \                                                           2                              3         \
  /     2\         |  /            /     2\   x*sin(2*x)\      /            /     2\   x*sin(2*x)\ |  sin(2*x)        /     2\            4*x*cos(2*x)   2*x *sin(2*x)|                 /     2\   3*cos(2*x)   6*x*sin(2*x)   6*x *cos(2*x)   3*x*sin(2*x)   4*x *sin(2*x)|
4*\1 + x /        *|2*|cos(2*x)*log\1 + x / + ----------|  - 3*|cos(2*x)*log\1 + x / + ----------|*|- -------- + 2*log\1 + x /*sin(2*x) - ------------ + -------------| - 2*cos(2*x)*log\1 + x / + ---------- - ------------ - ------------- - ------------ + -------------|
                   |  |                              2  |      |                              2  | |        2                                     2                2  |                                   2             2                2              2               3  |
                   |  \                         1 + x   /      \                         1 + x   / |   1 + x                                 1 + x         /     2\   |                              1 + x         1 + x         /     2\       /     2\        /     2\   |
                   \                                                                               \                                                       \1 + x /   /                                                          \1 + x /       \1 + x /        \1 + x /   /
4(x2+1)sin⁡(2x)(4x3sin⁡(2x)(x2+1)3−6x2cos⁡(2x)(x2+1)2−6xsin⁡(2x)x2+1−3xsin⁡(2x)(x2+1)2+2(xsin⁡(2x)x2+1+log⁡(x2+1)cos⁡(2x))3−3(xsin⁡(2x)x2+1+log⁡(x2+1)cos⁡(2x))(2x2sin⁡(2x)(x2+1)2−4xcos⁡(2x)x2+1+2log⁡(x2+1)sin⁡(2x)−sin⁡(2x)x2+1)−2log⁡(x2+1)cos⁡(2x)+3cos⁡(2x)x2+1)4 \left(x^{2} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{4 x^{3} \sin{\left(2 x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x^{2} \cos{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 x \sin{\left(2 x \right)}}{x^{2} + 1} - \frac{3 x \sin{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 2 \left(\frac{x \sin{\left(2 x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(2 x \right)}\right)^{3} - 3 \left(\frac{x \sin{\left(2 x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(2 x \right)}\right) \left(\frac{2 x^{2} \sin{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \cos{\left(2 x \right)}}{x^{2} + 1} + 2 \log{\left(x^{2} + 1 \right)} \sin{\left(2 x \right)} - \frac{\sin{\left(2 x \right)}}{x^{2} + 1}\right) - 2 \log{\left(x^{2} + 1 \right)} \cos{\left(2 x \right)} + \frac{3 \cos{\left(2 x \right)}}{x^{2} + 1}\right)
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Gráfico
Derivada de (x^2+1)^sin(2*x)
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