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y=2^sinxarcctgxx^4
Derivada de la función/ 2^sinx/ y=2^sinxarcctgxx^4

Derivada de y=2^sinxarcctgxx^4

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

Ha introducido [src] 
 sin(x)          4
2      *acot(x)*x
x4⋅2sin⁡(x)acot⁡(x)x^{4} \cdot 2^{\sin{\left(x \right)}} \operatorname{acot}{\left(x \right)} 
(2^sin(x)*acot(x))*x^4
Gráfica
02468-8-6-4-2-1010-25002500
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Primera derivada [src] 
   /   sin(x)                                \                       
 4 |  2          sin(x)                      |      sin(x)  3        
x *|- ------- + 2      *acot(x)*cos(x)*log(2)| + 4*2      *x *acot(x)
   |        2                                |                       
   \   1 + x                                 /
4⋅2sin⁡(x)x3acot⁡(x)+x4(2sin⁡(x)log⁡(2)cos⁡(x)acot⁡(x)−2sin⁡(x)x2+1)4 \cdot 2^{\sin{\left(x \right)}} x^{3} \operatorname{acot}{\left(x \right)} + x^{4} \left(2^{\sin{\left(x \right)}} \log{\left(2 \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x \right)} - \frac{2^{\sin{\left(x \right)}}}{x^{2} + 1}\right)
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Segunda derivada [src] 
 sin(x)  2 /              2 /     2*x      /     2                   \                  2*cos(x)*log(2)\       /    1                           \\
2      *x *|12*acot(x) - x *|- --------- + \- cos (x)*log(2) + sin(x)/*acot(x)*log(2) + ---------------| + 8*x*|- ------ + acot(x)*cos(x)*log(2)||
           |                |          2                                                          2    |       |       2                        ||
           |                |  /     2\                                                      1 + x     |       \  1 + x                         /|
           \                \  \1 + x /                                                                /                                         /
2sin⁡(x)x2(−x2(−2x(x2+1)2+(sin⁡(x)−log⁡(2)cos⁡2(x))log⁡(2)acot⁡(x)+2log⁡(2)cos⁡(x)x2+1)+8x(log⁡(2)cos⁡(x)acot⁡(x)−1x2+1)+12acot⁡(x))2^{\sin{\left(x \right)}} x^{2} \left(- x^{2} \left(- \frac{2 x}{\left(x^{2} + 1\right)^{2}} + \left(\sin{\left(x \right)} - \log{\left(2 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}{\left(x \right)} + \frac{2 \log{\left(2 \right)} \cos{\left(x \right)}}{x^{2} + 1}\right) + 8 x \left(\log{\left(2 \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x \right)} - \frac{1}{x^{2} + 1}\right) + 12 \operatorname{acot}{\left(x \right)}\right)
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Tercera derivada [src] 
          /                /    /         2 \                                                                                                                           \                                                                                                                               \
          |                |    |      4*x  |                                                                                                                           |                                                                                                                               |
          |                |  2*|-1 + ------|                                                                                                                           |                                                                                                                               |
          |                |    |          2|     /     2                   \                                                                                           |                                                                                                                               |
   sin(x) |              3 |    \     1 + x /   3*\- cos (x)*log(2) + sin(x)/*log(2)   /       2       2                     \                         6*x*cos(x)*log(2)|       2 /     2*x      /     2                   \                  2*cos(x)*log(2)\        /    1                           \|
x*2      *|24*acot(x) + x *|- --------------- + ------------------------------------ - \1 - cos (x)*log (2) + 3*log(2)*sin(x)/*acot(x)*cos(x)*log(2) + -----------------| - 12*x *|- --------- + \- cos (x)*log(2) + sin(x)/*acot(x)*log(2) + ---------------| + 36*x*|- ------ + acot(x)*cos(x)*log(2)||
          |                |             2                          2                                                                                              2    |         |          2                                                          2    |        |       2                        ||
          |                |     /     2\                      1 + x                                                                                       /     2\     |         |  /     2\                                                      1 + x     |        \  1 + x                         /|
          \                \     \1 + x /                                                                                                                  \1 + x /     /         \  \1 + x /                                                                /                                          /
2sin⁡(x)x(x3(6xlog⁡(2)cos⁡(x)(x2+1)2−(3log⁡(2)sin⁡(x)−log⁡(2)2cos⁡2(x)+1)log⁡(2)cos⁡(x)acot⁡(x)+3(sin⁡(x)−log⁡(2)cos⁡2(x))log⁡(2)x2+1−2(4x2x2+1−1)(x2+1)2)−12x2(−2x(x2+1)2+(sin⁡(x)−log⁡(2)cos⁡2(x))log⁡(2)acot⁡(x)+2log⁡(2)cos⁡(x)x2+1)+36x(log⁡(2)cos⁡(x)acot⁡(x)−1x2+1)+24acot⁡(x))2^{\sin{\left(x \right)}} x \left(x^{3} \left(\frac{6 x \log{\left(2 \right)} \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \left(3 \log{\left(2 \right)} \sin{\left(x \right)} - \log{\left(2 \right)}^{2} \cos^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x \right)} + \frac{3 \left(\sin{\left(x \right)} - \log{\left(2 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)}}{x^{2} + 1} - \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right) - 12 x^{2} \left(- \frac{2 x}{\left(x^{2} + 1\right)^{2}} + \left(\sin{\left(x \right)} - \log{\left(2 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}{\left(x \right)} + \frac{2 \log{\left(2 \right)} \cos{\left(x \right)}}{x^{2} + 1}\right) + 36 x \left(\log{\left(2 \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x \right)} - \frac{1}{x^{2} + 1}\right) + 24 \operatorname{acot}{\left(x \right)}\right)
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Gráfico
Derivada de y=2^sinxarcctgxx^4
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