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y=2^cosx*arcctg(5x^3)
Derivada de la función/ y=2^cosx/ y=2^cosx*arcctg(5x^3)

Derivada de y=2^cosx*arcctg(5x^3)

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

Ha introducido [src] 
 cos(x)     /   3\
2      *acot\5*x /
2cos⁡(x)acot⁡(5x3)2^{\cos{\left(x \right)}} \operatorname{acot}{\left(5 x^{3} \right)} 
2^cos(x)*acot(5*x^3)
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
      cos(x)  2                                   
  15*2      *x     cos(x)     /   3\              
- ------------- - 2      *acot\5*x /*log(2)*sin(x)
            6                                     
    1 + 25*x
−15⋅2cos⁡(x)x225x6+1−2cos⁡(x)log⁡(2)sin⁡(x)acot⁡(5x3)- \frac{15 \cdot 2^{\cos{\left(x \right)}} x^{2}}{25 x^{6} + 1} - 2^{\cos{\left(x \right)}} \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x^{3} \right)}
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Segunda derivada [src] 
        /                                                    /           6  \                      \
        |                                                    |       75*x   |                      |
        |                                               30*x*|-1 + ---------|                      |
        |                                                    |             6|       2              |
 cos(x) |/             2          \     /   3\               \     1 + 25*x /   30*x *log(2)*sin(x)|
2      *|\-cos(x) + sin (x)*log(2)/*acot\5*x /*log(2) + --------------------- + -------------------|
        |                                                             6                      6     |
        \                                                     1 + 25*x               1 + 25*x      /
2cos⁡(x)(30x2log⁡(2)sin⁡(x)25x6+1+30x(75x625x6+1−1)25x6+1+(log⁡(2)sin⁡2(x)−cos⁡(x))log⁡(2)acot⁡(5x3))2^{\cos{\left(x \right)}} \left(\frac{30 x^{2} \log{\left(2 \right)} \sin{\left(x \right)}}{25 x^{6} + 1} + \frac{30 x \left(\frac{75 x^{6}}{25 x^{6} + 1} - 1\right)}{25 x^{6} + 1} + \left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}{\left(5 x^{3} \right)}\right)
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Tercera derivada [src] 
        /     /           6            12  \                                                                                                                                                   \
        |     |      675*x      22500*x    |                                                                                                                     /           6  \              |
        |  30*|1 - --------- + ------------|                                                                                                                     |       75*x   |              |
        |     |            6              2|                                                                                                                90*x*|-1 + ---------|*log(2)*sin(x)|
        |     |    1 + 25*x    /        6\ |                                                                          2 /             2          \               |             6|              |
 cos(x) |     \                \1 + 25*x / /   /       2       2                     \     /   3\                 45*x *\-cos(x) + sin (x)*log(2)/*log(2)        \     1 + 25*x /              |
2      *|- --------------------------------- + \1 - log (2)*sin (x) + 3*cos(x)*log(2)/*acot\5*x /*log(2)*sin(x) - --------------------------------------- - -----------------------------------|
        |                      6                                                                                                         6                                       6             |
        \              1 + 25*x                                                                                                  1 + 25*x                                1 + 25*x              /
2cos⁡(x)(−45x2(log⁡(2)sin⁡2(x)−cos⁡(x))log⁡(2)25x6+1−90x(75x625x6+1−1)log⁡(2)sin⁡(x)25x6+1+(−log⁡(2)2sin⁡2(x)+3log⁡(2)cos⁡(x)+1)log⁡(2)sin⁡(x)acot⁡(5x3)−30(22500x12(25x6+1)2−675x625x6+1+1)25x6+1)2^{\cos{\left(x \right)}} \left(- \frac{45 x^{2} \left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)}}{25 x^{6} + 1} - \frac{90 x \left(\frac{75 x^{6}}{25 x^{6} + 1} - 1\right) \log{\left(2 \right)} \sin{\left(x \right)}}{25 x^{6} + 1} + \left(- \log{\left(2 \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(2 \right)} \cos{\left(x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x^{3} \right)} - \frac{30 \left(\frac{22500 x^{12}}{\left(25 x^{6} + 1\right)^{2}} - \frac{675 x^{6}}{25 x^{6} + 1} + 1\right)}{25 x^{6} + 1}\right)
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Gráfico
Derivada de y=2^cosx*arcctg(5x^3)
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