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y=arcctg^4x*cos7x^4

Derivada de y=arcctg^4x*cos7x^4

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
    4       4     
acot (x)*cos (7*x)
$$\cos^{4}{\left(7 x \right)} \operatorname{acot}^{4}{\left(x \right)}$$
acot(x)^4*cos(7*x)^4
Gráfica
Primera derivada [src]
                                         3       4     
         4       3                 4*acot (x)*cos (7*x)
- 28*acot (x)*cos (7*x)*sin(7*x) - --------------------
                                               2       
                                          1 + x        
$$- 28 \sin{\left(7 x \right)} \cos^{3}{\left(7 x \right)} \operatorname{acot}^{4}{\left(x \right)} - \frac{4 \cos^{4}{\left(7 x \right)} \operatorname{acot}^{3}{\left(x \right)}}{x^{2} + 1}$$
Segunda derivada [src]
                     /                                             2                                                      \
      2       2      |       2    /     2             2     \   cos (7*x)*(3 + 2*x*acot(x))   56*acot(x)*cos(7*x)*sin(7*x)|
4*acot (x)*cos (7*x)*|49*acot (x)*\- cos (7*x) + 3*sin (7*x)/ + --------------------------- + ----------------------------|
                     |                                                           2                            2           |
                     |                                                   /     2\                        1 + x            |
                     \                                                   \1 + x /                                         /
$$4 \left(49 \left(3 \sin^{2}{\left(7 x \right)} - \cos^{2}{\left(7 x \right)}\right) \operatorname{acot}^{2}{\left(x \right)} + \frac{56 \sin{\left(7 x \right)} \cos{\left(7 x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{\left(2 x \operatorname{acot}{\left(x \right)} + 3\right) \cos^{2}{\left(7 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cos^{2}{\left(7 x \right)} \operatorname{acot}^{2}{\left(x \right)}$$
Tercera derivada [src]
   /          /                         2     2                 \                                                                                                                                                            \                 
   |   3      |      2        3      4*x *acot (x)   9*x*acot(x)|                                                                                                                                                            |                 
   |cos (7*x)*|- acot (x) + ------ + ------------- + -----------|                                                                                                                                                            |                 
   |          |                  2            2              2  |                                                                 2    /     2             2     \                  2                                        |                 
   |          \             1 + x        1 + x          1 + x   /           3    /       2             2     \            294*acot (x)*\- cos (7*x) + 3*sin (7*x)/*cos(7*x)   42*cos (7*x)*(3 + 2*x*acot(x))*acot(x)*sin(7*x)|                 
-8*|------------------------------------------------------------- + 343*acot (x)*\- 5*cos (7*x) + 3*sin (7*x)/*sin(7*x) + ------------------------------------------------- + -----------------------------------------------|*acot(x)*cos(7*x)
   |                                  2                                                                                                              2                                                   2                   |                 
   |                          /     2\                                                                                                          1 + x                                            /     2\                    |                 
   \                          \1 + x /                                                                                                                                                           \1 + x /                    /                 
$$- 8 \left(343 \left(3 \sin^{2}{\left(7 x \right)} - 5 \cos^{2}{\left(7 x \right)}\right) \sin{\left(7 x \right)} \operatorname{acot}^{3}{\left(x \right)} + \frac{294 \left(3 \sin^{2}{\left(7 x \right)} - \cos^{2}{\left(7 x \right)}\right) \cos{\left(7 x \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{42 \left(2 x \operatorname{acot}{\left(x \right)} + 3\right) \sin{\left(7 x \right)} \cos^{2}{\left(7 x \right)} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{9 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{3}{x^{2} + 1}\right) \cos^{3}{\left(7 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cos{\left(7 x \right)} \operatorname{acot}{\left(x \right)}$$
Gráfico
Derivada de y=arcctg^4x*cos7x^4