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

Derivada de y=x*cos^3arctglnx

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

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Solución

Ha introducido [src] 
     3                
x*cos (x)*atan(log(x))
xcos⁡3(x)atan⁡(log⁡(x))x \cos^{3}{\left(x \right)} \operatorname{atan}{\left(\log{\left(x \right)} \right)} 
(x*cos(x)^3)*atan(log(x))
Gráfica
02468-8-6-4-2-1010-2525
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Trazar el gráfico f'(x)
Primera derivada [src] 
     3                                                   
  cos (x)     /   3             2          \             
----------- + \cos (x) - 3*x*cos (x)*sin(x)/*atan(log(x))
       2                                                 
1 + log (x)
(−3xsin⁡(x)cos⁡2(x)+cos⁡3(x))atan⁡(log⁡(x))+cos⁡3(x)log⁡(x)2+1\left(- 3 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{3}{\left(x \right)}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \frac{\cos^{3}{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}
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Segunda derivada [src] 
/                                                                  2    /      2*log(x) \                                  \       
|                                                               cos (x)*|1 + -----------|                                  |       
|                                                                       |           2   |                                  |       
|  /  /     2           2   \                  \                        \    1 + log (x)/   2*(-cos(x) + 3*x*sin(x))*cos(x)|       
|3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*atan(log(x)) - ------------------------- - -------------------------------|*cos(x)
|                                                                      /       2   \                  /       2   \        |       
\                                                                    x*\1 + log (x)/                x*\1 + log (x)/        /
(3(x(2sin⁡2(x)−cos⁡2(x))−2sin⁡(x)cos⁡(x))atan⁡(log⁡(x))−(1+2log⁡(x)log⁡(x)2+1)cos⁡2(x)x(log⁡(x)2+1)−2(3xsin⁡(x)−cos⁡(x))cos⁡(x)x(log⁡(x)2+1))cos⁡(x)\left(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(\log{\left(x \right)} \right)} - \frac{\left(1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}\right) \cos^{2}{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)} - \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)}\right) \cos{\left(x \right)}
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Tercera derivada [src] 
                                                                                                       /                                       2      \                                                                                                              
                                                                                                  3    |         1          3*log(x)      4*log (x)   |                                                                                                              
                                                                                             2*cos (x)*|1 - ----------- + ----------- + --------------|                                                                 2    /      2*log(x) \                       
                                                                                                       |           2             2                   2|                                                            3*cos (x)*|1 + -----------|*(-cos(x) + 3*x*sin(x))
                                                                                                       |    1 + log (x)   1 + log (x)   /       2   \ |     /  /     2           2   \                  \                    |           2   |                       
    /    /     2           2   \            /       2           2   \       \                          \                                \1 + log (x)/ /   9*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*cos(x)             \    1 + log (x)/                       
- 3*\- 3*\- cos (x) + 2*sin (x)/*cos(x) + x*\- 7*cos (x) + 2*sin (x)/*sin(x)/*atan(log(x)) + ---------------------------------------------------------- + ------------------------------------------------------ + --------------------------------------------------
                                                                                                                   2 /       2   \                                             /       2   \                                         2 /       2   \                 
                                                                                                                  x *\1 + log (x)/                                           x*\1 + log (x)/                                        x *\1 + log (x)/
−3(x(2sin⁡2(x)−7cos⁡2(x))sin⁡(x)−3(2sin⁡2(x)−cos⁡2(x))cos⁡(x))atan⁡(log⁡(x))+9(x(2sin⁡2(x)−cos⁡2(x))−2sin⁡(x)cos⁡(x))cos⁡(x)x(log⁡(x)2+1)+3(1+2log⁡(x)log⁡(x)2+1)(3xsin⁡(x)−cos⁡(x))cos⁡2(x)x2(log⁡(x)2+1)+2(1+3log⁡(x)log⁡(x)2+1−1log⁡(x)2+1+4log⁡(x)2(log⁡(x)2+1)2)cos⁡3(x)x2(log⁡(x)2+1)- 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(\log{\left(x \right)} \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 \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{3 \left(1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}\right) \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{2 \left(1 + \frac{3 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1} - \frac{1}{\log{\left(x \right)}^{2} + 1} + \frac{4 \log{\left(x \right)}^{2}}{\left(\log{\left(x \right)}^{2} + 1\right)^{2}}\right) \cos^{3}{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)}
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Gráfico
Derivada de y=x*cos^3arctglnx
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