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y=(x*cos^3)arctglnx
Derivada de la función/ cos^3/ tglnx/ arctg/ y=(x*cos^3)arctglnx

Derivada de y=(x*cos^3)arctglnx

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

Ha introducido [src] 
     3                  
x*cos (x)*atan(x)*log(x)
xcos⁡3(x)atan⁡(x)log⁡(x)x \cos^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)} \log{\left(x \right)} 
((x*cos(x)^3)*atan(x))*log(x)
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                  /                                              3   \       
   3              |/   3             2          \           x*cos (x)|       
cos (x)*atan(x) + |\cos (x) - 3*x*cos (x)*sin(x)/*atan(x) + ---------|*log(x)
                  |                                                2 |       
                  \                                           1 + x  /
(xcos⁡3(x)x2+1+(−3xsin⁡(x)cos⁡2(x)+cos⁡3(x))atan⁡(x))log⁡(x)+cos⁡3(x)atan⁡(x)\left(\frac{x \cos^{3}{\left(x \right)}}{x^{2} + 1} + \left(- 3 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{3}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)} + \cos^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}
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Segunda derivada [src] 
/                                                                                                                                            /                                  x*cos(x)\       \       
|                                                                                                                                          2*|-(-cos(x) + 3*x*sin(x))*atan(x) + --------|*cos(x)|       
|  /                                                               2    2                                     \             2                |                                        2 |       |       
|  |    /  /     2           2   \                  \           2*x *cos (x)   2*(-cos(x) + 3*x*sin(x))*cos(x)|          cos (x)*atan(x)     \                                   1 + x  /       |       
|- |- 3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*atan(x) + ------------ + -------------------------------|*log(x) - --------------- + -----------------------------------------------------|*cos(x)
|  |                                                                     2                       2            |                 x                                    x                          |       
|  |                                                             /     2\                   1 + x             |                                                                                 |       
\  \                                                             \1 + x /                                     /                                                                                 /
(−(2x2cos⁡2(x)(x2+1)2−3(x(2sin⁡2(x)−cos⁡2(x))−2sin⁡(x)cos⁡(x))atan⁡(x)+2(3xsin⁡(x)−cos⁡(x))cos⁡(x)x2+1)log⁡(x)+2(xcos⁡(x)x2+1−(3xsin⁡(x)−cos⁡(x))atan⁡(x))cos⁡(x)x−cos⁡2(x)atan⁡(x)x)cos⁡(x)\left(- \left(\frac{2 x^{2} \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 3 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} + 1}\right) \log{\left(x \right)} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{x^{2} + 1} - \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}\right) \cos{\left(x \right)}}{x} - \frac{\cos^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) \cos{\left(x \right)}
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Tercera derivada [src] 
                                                                                                                                                                                                                             /                                                               2    2                                     \                                                                                    
/                                                                                                                                                             /         2 \                                     \            |    /  /     2           2   \                  \           2*x *cos (x)   2*(-cos(x) + 3*x*sin(x))*cos(x)|                                                                                    
|                                                                                                                                                        3    |      4*x  |                                     |          3*|- 3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*atan(x) + ------------ + -------------------------------|*cos(x)        2    /                                  x*cos(x)\                    
|                                                                                                                                                 2*x*cos (x)*|-1 + ------|                                     |            |                                                                     2                       2            |          3*cos (x)*|-(-cos(x) + 3*x*sin(x))*atan(x) + --------|                    
|                                                                                          /  /     2           2   \                  \                      |          2|          2                          |            |                                                             /     2\                   1 + x             |                    |                                        2 |        3           
|    /    /     2           2   \            /       2           2   \       \           9*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*cos(x)               \     1 + x /   6*x*cos (x)*(-cos(x) + 3*x*sin(x))|            \                                                             \1 + x /                                     /                    \                                   1 + x  /   2*cos (x)*atan(x)
|- 3*\- 3*\- cos (x) + 2*sin (x)/*cos(x) + x*\- 7*cos (x) + 2*sin (x)/*sin(x)/*atan(x) + ------------------------------------------------------ + ------------------------- + ----------------------------------|*log(x) - --------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------ + -----------------
|                                                                                                                     2                                           2                               2             |                                                                    x                                                                                        2                                      2       
|                                                                                                                1 + x                                    /     2\                        /     2\              |                                                                                                                                                            x                                      x        
\                                                                                                                                                         \1 + x /                        \1 + x /              /
(6x(3xsin⁡(x)−cos⁡(x))cos⁡2(x)(x2+1)2+2x(4x2x2+1−1)cos⁡3(x)(x2+1)2−3(x(2sin⁡2(x)−7cos⁡2(x))sin⁡(x)−3(2sin⁡2(x)−cos⁡2(x))cos⁡(x))atan⁡(x)+9(x(2sin⁡2(x)−cos⁡2(x))−2sin⁡(x)cos⁡(x))cos⁡(x)x2+1)log⁡(x)−3(2x2cos⁡2(x)(x2+1)2−3(x(2sin⁡2(x)−cos⁡2(x))−2sin⁡(x)cos⁡(x))atan⁡(x)+2(3xsin⁡(x)−cos⁡(x))cos⁡(x)x2+1)cos⁡(x)x−3(xcos⁡(x)x2+1−(3xsin⁡(x)−cos⁡(x))atan⁡(x))cos⁡2(x)x2+2cos⁡3(x)atan⁡(x)x2\left(\frac{6 x \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 3 \left(x \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} - 3 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{9 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} + 1}\right) \log{\left(x \right)} - \frac{3 \left(\frac{2 x^{2} \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 3 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} + 1}\right) \cos{\left(x \right)}}{x} - \frac{3 \left(\frac{x \cos{\left(x \right)}}{x^{2} + 1} - \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{x^{2}} + \frac{2 \cos^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}}
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Gráfico
Derivada de y=(x*cos^3)arctglnx
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