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y=√cot7(3x)+arcos3(x^4)
Derivada de la función/ (x^4)/ y=√cot7(3x)+arcos3(x^4)

Derivada de y=√cot7(3x)+arcos3(x^4)

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

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Solución

Ha introducido [src] 
            7            
  __________        3/ 4\
\/ cot(3*x)   + acos \x /
(cot⁡(3x))7+acos⁡3(x4)\left(\sqrt{\cot{\left(3 x \right)}}\right)^{7} + \operatorname{acos}^{3}{\left(x^{4} \right)} 
(sqrt(cot(3*x)))^7 + acos(x^4)^3
Gráfica
02468-8-6-4-2-1010-25002500
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Primera derivada [src] 
                                  /           2     \
                         7/2      |  3   3*cot (3*x)|
      3     2/ 4\   7*cot   (3*x)*|- - - -----------|
  12*x *acos \x /                 \  2        2     /
- --------------- + ---------------------------------
       ________                  cot(3*x)            
      /      8                                       
    \/  1 - x
−12x3acos⁡2(x4)1−x8+7(−3cot⁡2(3x)2−32)cot⁡72(3x)cot⁡(3x)- \frac{12 x^{3} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} + \frac{7 \left(- \frac{3 \cot^{2}{\left(3 x \right)}}{2} - \frac{3}{2}\right) \cot^{\frac{7}{2}}{\left(3 x \right)}}{\cot{\left(3 x \right)}}
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Segunda derivada [src] 
  /                                                    2                                                                  \
  |                                     /       2     \     3/2            6     / 4\       10     2/ 4\       2     2/ 4\|
  |      7/2      /       2     \   105*\1 + cot (3*x)/ *cot   (3*x)   32*x *acos\x /   16*x  *acos \x /   12*x *acos \x /|
3*|21*cot   (3*x)*\1 + cot (3*x)/ + -------------------------------- - -------------- - ---------------- - ---------------|
  |                                                4                            8                 3/2           ________  |
  |                                                                       -1 + x          /     8\             /      8   |
  \                                                                                       \1 - x /           \/  1 - x    /
3(−16x10acos⁡2(x4)(1−x8)32−32x6acos⁡(x4)x8−1−12x2acos⁡2(x4)1−x8+105(cot⁡2(3x)+1)2cot⁡32(3x)4+21(cot⁡2(3x)+1)cot⁡72(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{105 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \cot^{\frac{3}{2}}{\left(3 x \right)}}{4} + 21 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot^{\frac{7}{2}}{\left(3 x \right)}\right)
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Tercera derivada [src] 
  /                                                                      2                                  3                                                                                                          \
  |          9                                            /       2     \     5/2            /       2     \    __________        5     / 4\        9     2/ 4\        17     2/ 4\            2/ 4\        13     / 4\|
  |     128*x             9/2      /       2     \   1071*\1 + cot (3*x)/ *cot   (3*x)   945*\1 + cot (3*x)/ *\/ cot(3*x)    288*x *acos\x /   208*x *acos \x /   192*x  *acos \x /   24*x*acos \x /   384*x  *acos\x /|
3*|- ----------- - 126*cot   (3*x)*\1 + cot (3*x)/ - --------------------------------- - --------------------------------- - --------------- - ---------------- - ----------------- - -------------- + ----------------|
  |          3/2                                                     2                                   8                             8                 3/2                 5/2          ________                 2   |
  |  /     8\                                                                                                                    -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−x8−945(cot⁡2(3x)+1)3cot⁡(3x)8−1071(cot⁡2(3x)+1)2cot⁡52(3x)2−126(cot⁡2(3x)+1)cot⁡92(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{945 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{3} \sqrt{\cot{\left(3 x \right)}}}{8} - \frac{1071 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \cot^{\frac{5}{2}}{\left(3 x \right)}}{2} - 126 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot^{\frac{9}{2}}{\left(3 x \right)}\right)
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Gráfico
Derivada de y=√cot7(3x)+arcos3(x^4)
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