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y=2^sinx×arcctg(x^4)
Derivada de la función/ (x^4)/ 2^sinx/ y=2^sinx×arcctg(x^4)

Derivada de y=2^sinx×arcctg(x^4)

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

Ha introducido [src] 
 sin(x)     / 4\
2      *acot\x /
2sin⁡(x)acot⁡(x4)2^{\sin{\left(x \right)}} \operatorname{acot}{\left(x^{4} \right)} 
2^sin(x)*acot(x^4)
Gráfica
02468-8-6-4-2-10105-5
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Primera derivada [src] 
     sin(x)  3                                 
  4*2      *x     sin(x)     / 4\              
- ------------ + 2      *acot\x /*cos(x)*log(2)
          8                                    
     1 + x
−4⋅2sin⁡(x)x3x8+1+2sin⁡(x)log⁡(2)cos⁡(x)acot⁡(x4)- \frac{4 \cdot 2^{\sin{\left(x \right)}} x^{3}}{x^{8} + 1} + 2^{\sin{\left(x \right)}} \log{\left(2 \right)} \cos{\left(x \right)} \operatorname{acot}{\left(x^{4} \right)}
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Segunda derivada [src] 
        /                                                     /         8 \                     \
        |                                                   2 |      8*x  |                     |
        |                                                4*x *|-3 + ------|                     |
        |                                                     |          8|      3              |
 sin(x) |  /     2                   \     / 4\               \     1 + x /   8*x *cos(x)*log(2)|
2      *|- \- cos (x)*log(2) + sin(x)/*acot\x /*log(2) + ------------------ - ------------------|
        |                                                           8                    8      |
        \                                                      1 + x                1 + x       /
2sin⁡(x)(−8x3log⁡(2)cos⁡(x)x8+1+4x2(8x8x8+1−3)x8+1−(sin⁡(x)−log⁡(2)cos⁡2(x))log⁡(2)acot⁡(x4))2^{\sin{\left(x \right)}} \left(- \frac{8 x^{3} \log{\left(2 \right)} \cos{\left(x \right)}}{x^{8} + 1} + \frac{4 x^{2} \left(\frac{8 x^{8}}{x^{8} + 1} - 3\right)}{x^{8} + 1} - \left(\sin{\left(x \right)} - \log{\left(2 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}{\left(x^{4} \right)}\right)
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Tercera derivada [src] 
        /      /        8          16 \                                                                                                                                                \
        |      |    52*x       64*x   |                                                                                                                     /         8 \              |
        |  8*x*|3 - ------ + ---------|                                                                                                                   2 |      8*x  |              |
        |      |         8           2|                                                                                                               12*x *|-3 + ------|*cos(x)*log(2)|
        |      |    1 + x    /     8\ |                                                                        3 /     2                   \                |          8|              |
 sin(x) |      \             \1 + x / /   /       2       2                     \     / 4\                 12*x *\- cos (x)*log(2) + sin(x)/*log(2)         \     1 + x /              |
2      *|- ---------------------------- - \1 - cos (x)*log (2) + 3*log(2)*sin(x)/*acot\x /*cos(x)*log(2) + ---------------------------------------- + ---------------------------------|
        |                  8                                                                                                     8                                       8             |
        \             1 + x                                                                                                 1 + x                                   1 + x              /
2sin⁡(x)(12x3(sin⁡(x)−log⁡(2)cos⁡2(x))log⁡(2)x8+1+12x2(8x8x8+1−3)log⁡(2)cos⁡(x)x8+1−8x(64x16(x8+1)2−52x8x8+1+3)x8+1−(3log⁡(2)sin⁡(x)−log⁡(2)2cos⁡2(x)+1)log⁡(2)cos⁡(x)acot⁡(x4))2^{\sin{\left(x \right)}} \left(\frac{12 x^{3} \left(\sin{\left(x \right)} - \log{\left(2 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)}}{x^{8} + 1} + \frac{12 x^{2} \left(\frac{8 x^{8}}{x^{8} + 1} - 3\right) \log{\left(2 \right)} \cos{\left(x \right)}}{x^{8} + 1} - \frac{8 x \left(\frac{64 x^{16}}{\left(x^{8} + 1\right)^{2}} - \frac{52 x^{8}}{x^{8} + 1} + 3\right)}{x^{8} + 1} - \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^{4} \right)}\right)
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Gráfico
Derivada de y=2^sinx×arcctg(x^4)
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