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(x*x+1)^(cos3x)
Derivada de la función/ cos3x/ x*x+1/ (x*x+1)^(cos3x)

Derivada de (x*x+1)^(cos3x)

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

Ha introducido [src] 
         cos(3*x)
(x*x + 1)
(xx+1)cos⁡(3x)\left(x x + 1\right)^{\cos{\left(3 x \right)}} 
(x*x + 1)^cos(3*x)
Solución detallada

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

    Perola derivada

    (log⁡(cos⁡(3x))+1)cos⁡cos⁡(3x)(3x)\left(\log{\left(\cos{\left(3 x \right)} \right)} + 1\right) \cos^{\cos{\left(3 x \right)}}{\left(3 x \right)}

Respuesta:

(log⁡(cos⁡(3x))+1)cos⁡cos⁡(3x)(3x)\left(\log{\left(\cos{\left(3 x \right)} \right)} + 1\right) \cos^{\cos{\left(3 x \right)}}{\left(3 x \right)}

Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         cos(3*x) /                           2*x*cos(3*x)\
(x*x + 1)        *|-3*log(x*x + 1)*sin(3*x) + ------------|
                  \                             x*x + 1   /
(xx+1)cos⁡(3x)(2xcos⁡(3x)xx+1−3log⁡(xx+1)sin⁡(3x))\left(x x + 1\right)^{\cos{\left(3 x \right)}} \left(\frac{2 x \cos{\left(3 x \right)}}{x x + 1} - 3 \log{\left(x x + 1 \right)} \sin{\left(3 x \right)}\right)
Simplificar
Segunda derivada [src] 
        cos(3*x) /                                         2                                                            2         \
/     2\         |/       /     2\            2*x*cos(3*x)\                  /     2\   2*cos(3*x)   12*x*sin(3*x)   4*x *cos(3*x)|
\1 + x /        *||- 3*log\1 + x /*sin(3*x) + ------------|  - 9*cos(3*x)*log\1 + x / + ---------- - ------------- - -------------|
                 ||                                   2   |                                    2              2                2  |
                 |\                              1 + x    /                               1 + x          1 + x         /     2\   |
                 \                                                                                                     \1 + x /   /
(x2+1)cos⁡(3x)(−4x2cos⁡(3x)(x2+1)2−12xsin⁡(3x)x2+1+(2xcos⁡(3x)x2+1−3log⁡(x2+1)sin⁡(3x))2−9log⁡(x2+1)cos⁡(3x)+2cos⁡(3x)x2+1)\left(x^{2} + 1\right)^{\cos{\left(3 x \right)}} \left(- \frac{4 x^{2} \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{12 x \sin{\left(3 x \right)}}{x^{2} + 1} + \left(\frac{2 x \cos{\left(3 x \right)}}{x^{2} + 1} - 3 \log{\left(x^{2} + 1 \right)} \sin{\left(3 x \right)}\right)^{2} - 9 \log{\left(x^{2} + 1 \right)} \cos{\left(3 x \right)} + \frac{2 \cos{\left(3 x \right)}}{x^{2} + 1}\right)
Simplificar
Tercera derivada [src] 
        cos(3*x) /                                         3                                                             /                                           2                         \                                                                 3                2         \
/     2\         |/       /     2\            2*x*cos(3*x)\    18*sin(3*x)     /       /     2\            2*x*cos(3*x)\ |  2*cos(3*x)                 /     2\   4*x *cos(3*x)   12*x*sin(3*x)|         /     2\            54*x*cos(3*x)   12*x*cos(3*x)   16*x *cos(3*x)   36*x *sin(3*x)|
\1 + x /        *||- 3*log\1 + x /*sin(3*x) + ------------|  - ----------- - 3*|- 3*log\1 + x /*sin(3*x) + ------------|*|- ---------- + 9*cos(3*x)*log\1 + x / + ------------- + -------------| + 27*log\1 + x /*sin(3*x) - ------------- - ------------- + -------------- + --------------|
                 ||                                   2   |            2       |                                   2   | |         2                                        2              2   |                                      2                2               3                2   |
                 |\                              1 + x    /       1 + x        \                              1 + x    / |    1 + x                                 /     2\          1 + x    |                                 1 + x         /     2\        /     2\         /     2\    |
                 \                                                                                                       \                                          \1 + x /                   /                                               \1 + x /        \1 + x /         \1 + x /    /
(x2+1)cos⁡(3x)(16x3cos⁡(3x)(x2+1)3+36x2sin⁡(3x)(x2+1)2−54xcos⁡(3x)x2+1−12xcos⁡(3x)(x2+1)2+(2xcos⁡(3x)x2+1−3log⁡(x2+1)sin⁡(3x))3−3(2xcos⁡(3x)x2+1−3log⁡(x2+1)sin⁡(3x))(4x2cos⁡(3x)(x2+1)2+12xsin⁡(3x)x2+1+9log⁡(x2+1)cos⁡(3x)−2cos⁡(3x)x2+1)+27log⁡(x2+1)sin⁡(3x)−18sin⁡(3x)x2+1)\left(x^{2} + 1\right)^{\cos{\left(3 x \right)}} \left(\frac{16 x^{3} \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{36 x^{2} \sin{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{54 x \cos{\left(3 x \right)}}{x^{2} + 1} - \frac{12 x \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \cos{\left(3 x \right)}}{x^{2} + 1} - 3 \log{\left(x^{2} + 1 \right)} \sin{\left(3 x \right)}\right)^{3} - 3 \left(\frac{2 x \cos{\left(3 x \right)}}{x^{2} + 1} - 3 \log{\left(x^{2} + 1 \right)} \sin{\left(3 x \right)}\right) \left(\frac{4 x^{2} \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{12 x \sin{\left(3 x \right)}}{x^{2} + 1} + 9 \log{\left(x^{2} + 1 \right)} \cos{\left(3 x \right)} - \frac{2 \cos{\left(3 x \right)}}{x^{2} + 1}\right) + 27 \log{\left(x^{2} + 1 \right)} \sin{\left(3 x \right)} - \frac{18 \sin{\left(3 x \right)}}{x^{2} + 1}\right)
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Gráfico
Derivada de (x*x+1)^(cos3x)
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