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y=2x^cos(6x)*arctg5x^3

Derivada de y=2x^cos(6x)*arctg5x^3

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

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Solución

Ha introducido [src]
   cos(6*x)     3     
2*x        *atan (5*x)
$$2 x^{\cos{\left(6 x \right)}} \operatorname{atan}^{3}{\left(5 x \right)}$$
(2*x^cos(6*x))*atan(5*x)^3
Gráfica
Primera derivada [src]
                                                            cos(6*x)     2     
   cos(6*x)     3      /cos(6*x)                    \   30*x        *atan (5*x)
2*x        *atan (5*x)*|-------- - 6*log(x)*sin(6*x)| + -----------------------
                       \   x                        /                  2       
                                                               1 + 25*x        
$$2 x^{\cos{\left(6 x \right)}} \left(- 6 \log{\left(x \right)} \sin{\left(6 x \right)} + \frac{\cos{\left(6 x \right)}}{x}\right) \operatorname{atan}^{3}{\left(5 x \right)} + \frac{30 x^{\cos{\left(6 x \right)}} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1}$$
Segunda derivada [src]
             /                                                                                                                               /  cos(6*x)                    \          \          
             |           /                                  2                                              \                              30*|- -------- + 6*log(x)*sin(6*x)|*atan(5*x)|          
    cos(6*x) |    2      |  /  cos(6*x)                    \    cos(6*x)   12*sin(6*x)                     |   150*(-1 + 5*x*atan(5*x))      \     x                        /          |          
-2*x        *|atan (5*x)*|- |- -------- + 6*log(x)*sin(6*x)|  + -------- + ----------- + 36*cos(6*x)*log(x)| + ------------------------ + ---------------------------------------------|*atan(5*x)
             |           |  \     x                        /        2           x                          |                    2                                   2                  |          
             |           \                                         x                                       /         /        2\                            1 + 25*x                   |          
             \                                                                                                       \1 + 25*x /                                                       /          
$$- 2 x^{\cos{\left(6 x \right)}} \left(\left(- \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right)^{2} + 36 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{12 \sin{\left(6 x \right)}}{x} + \frac{\cos{\left(6 x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(5 x \right)} + \frac{30 \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right) \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{150 \left(5 x \operatorname{atan}{\left(5 x \right)} - 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(5 x \right)}$$
Tercera derivada [src]
            /                                                                                                                                                                                                          /                                               2     2     \                 /                                  2                                              \                                                                      \
            |                                                                                                                                                                                                          |    1           2        30*x*atan(5*x)   100*x *atan (5*x)|          2      |  /  cos(6*x)                    \    cos(6*x)   12*sin(6*x)                     |                                                                      |
            |                                                                                                                                                                                                      750*|--------- - atan (5*x) - -------------- + -----------------|   45*atan (5*x)*|- |- -------- + 6*log(x)*sin(6*x)|  + -------- + ----------- + 36*cos(6*x)*log(x)|                            /  cos(6*x)                    \          |
            |           /                                  3                                                                                                                                                   \       |        2                          2                  2    |                 |  \     x                        /        2           x                          |   450*(-1 + 5*x*atan(5*x))*|- -------- + 6*log(x)*sin(6*x)|*atan(5*x)|
   cos(6*x) |    3      |  /  cos(6*x)                    \    108*cos(6*x)   2*cos(6*x)     /  cos(6*x)                    \ /cos(6*x)   12*sin(6*x)                     \   18*sin(6*x)                      |       \1 + 25*x                   1 + 25*x           1 + 25*x     /                 \                                         x                                       /                            \     x                        /          |
2*x        *|atan (5*x)*|- |- -------- + 6*log(x)*sin(6*x)|  - ------------ + ---------- + 3*|- -------- + 6*log(x)*sin(6*x)|*|-------- + ----------- + 36*cos(6*x)*log(x)| + ----------- + 216*log(x)*sin(6*x)| + ----------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------|
            |           |  \     x                        /         x              3         \     x                        / |    2           x                          |         2                          |                                         2                                                                                 2                                                                                      2                           |
            |           \                                                         x                                           \   x                                       /        x                           /                              /        2\                                                                          1 + 25*x                                                                            /        2\                            |
            \                                                                                                                                                                                                                                 \1 + 25*x /                                                                                                                                                              \1 + 25*x /                            /
$$2 x^{\cos{\left(6 x \right)}} \left(\left(- \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right)^{3} + 3 \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right) \left(36 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{12 \sin{\left(6 x \right)}}{x} + \frac{\cos{\left(6 x \right)}}{x^{2}}\right) + 216 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{108 \cos{\left(6 x \right)}}{x} + \frac{18 \sin{\left(6 x \right)}}{x^{2}} + \frac{2 \cos{\left(6 x \right)}}{x^{3}}\right) \operatorname{atan}^{3}{\left(5 x \right)} - \frac{45 \left(- \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right)^{2} + 36 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{12 \sin{\left(6 x \right)}}{x} + \frac{\cos{\left(6 x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{450 \left(5 x \operatorname{atan}{\left(5 x \right)} - 1\right) \left(6 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{\cos{\left(6 x \right)}}{x}\right) \operatorname{atan}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{750 \left(\frac{100 x^{2} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{30 x \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{atan}^{2}{\left(5 x \right)} + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right)$$
Gráfico
Derivada de y=2x^cos(6x)*arctg5x^3