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y=√cot3x+arcos3(x^4)
Derivada de la función/ (x^4)/ y=√cot3x+arcos3(x^4)

Derivada de y=√cot3x+arcos3(x^4)

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

Ha introducido [src] 
  __________       3/ 4\
\/ cot(3*x)  + acos \x /
cot⁡(3x)+acos⁡3(x4)\sqrt{\cot{\left(3 x \right)}} + \operatorname{acos}^{3}{\left(x^{4} \right)} 
sqrt(cot(3*x)) + acos(x^4)^3
Gráfica
02468-8-6-4-2-1010-2020
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Primera derivada [src] 
           2                       
  3   3*cot (3*x)                  
- - - -----------       3     2/ 4\
  2        2        12*x *acos \x /
----------------- - ---------------
     __________          ________  
   \/ cot(3*x)          /      8   
                      \/  1 - x
−12x3acos⁡2(x4)1−x8+−3cot⁡2(3x)2−32cot⁡(3x)- \frac{12 x^{3} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} + \frac{- \frac{3 \cot^{2}{\left(3 x \right)}}{2} - \frac{3}{2}}{\sqrt{\cot{\left(3 x \right)}}}
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Segunda derivada [src] 
  /                                                  2                                                      \
  |                                   /       2     \        6     / 4\       10     2/ 4\       2     2/ 4\|
  |    __________ /       2     \   3*\1 + cot (3*x)/    32*x *acos\x /   16*x  *acos \x /   12*x *acos \x /|
3*|3*\/ cot(3*x) *\1 + cot (3*x)/ - ------------------ - -------------- - ---------------- - ---------------|
  |                                        3/2                    8                 3/2           ________  |
  |                                   4*cot   (3*x)         -1 + x          /     8\             /      8   |
  \                                                                         \1 - x /           \/  1 - x    /
3(−16x10acos⁡2(x4)(1−x8)32−32x6acos⁡(x4)x8−1−12x2acos⁡2(x4)1−x8−3(cot⁡2(3x)+1)24cot⁡32(3x)+3(cot⁡2(3x)+1)cot⁡(3x))3 \left(- \frac{16 x^{10} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{32 x^{6} \operatorname{acos}{\left(x^{4} \right)}}{x^{8} - 1} - \frac{12 x^{2} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} - \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{4 \cot^{\frac{3}{2}}{\left(3 x \right)}} + 3 \left(\cot^{2}{\left(3 x \right)} + 1\right) \sqrt{\cot{\left(3 x \right)}}\right)
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Tercera derivada [src] 
  /                                                                   3                    2                                                                                             \
  |          9                                         /       2     \      /       2     \         5     / 4\        9     2/ 4\        17     2/ 4\            2/ 4\        13     / 4\|
  |     128*x            3/2      /       2     \   27*\1 + cot (3*x)/    9*\1 + cot (3*x)/    288*x *acos\x /   208*x *acos \x /   192*x  *acos \x /   24*x*acos \x /   384*x  *acos\x /|
3*|- ----------- - 18*cot   (3*x)*\1 + cot (3*x)/ - ------------------- + ------------------ - --------------- - ---------------- - ----------------- - -------------- + ----------------|
  |          3/2                                            5/2                 __________               8                 3/2                 5/2          ________                 2   |
  |  /     8\                                          8*cot   (3*x)        2*\/ cot(3*x)          -1 + x          /     8\            /     8\            /      8         /      8\    |
  \  \1 - x /                                                                                                      \1 - x /            \1 - x /          \/  1 - x          \-1 + x /    /
3(−192x17acos⁡2(x4)(1−x8)52+384x13acos⁡(x4)(x8−1)2−208x9acos⁡2(x4)(1−x8)32−128x9(1−x8)32−288x5acos⁡(x4)x8−1−24xacos⁡2(x4)1−x8−27(cot⁡2(3x)+1)38cot⁡52(3x)+9(cot⁡2(3x)+1)22cot⁡(3x)−18(cot⁡2(3x)+1)cot⁡32(3x))3 \left(- \frac{192 x^{17} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{5}{2}}} + \frac{384 x^{13} \operatorname{acos}{\left(x^{4} \right)}}{\left(x^{8} - 1\right)^{2}} - \frac{208 x^{9} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{128 x^{9}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{288 x^{5} \operatorname{acos}{\left(x^{4} \right)}}{x^{8} - 1} - \frac{24 x \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} - \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3}}{8 \cot^{\frac{5}{2}}{\left(3 x \right)}} + \frac{9 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{2 \sqrt{\cot{\left(3 x \right)}}} - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot^{\frac{3}{2}}{\left(3 x \right)}\right)
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Gráfico
Derivada de y=√cot3x+arcos3(x^4)
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