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y=√cot^73x+arcos3(x^4)
Derivada de la función/ (x^4)/ y=√cot^73x+arcos3(x^4)

Derivada de y=√cot^73x+arcos3(x^4)

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

Ha introducido [src] 
          73            
  ________         3/ 4\
\/ cot(x)    + acos \x /
(cot⁡(x))73+acos⁡3(x4)\left(\sqrt{\cot{\left(x \right)}}\right)^{73} + \operatorname{acos}^{3}{\left(x^{4} \right)} 
(sqrt(cot(x)))^73 + acos(x^4)^3
Gráfica
02468-8-6-4-2-1010-2e7610e75
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                  /         2   \
                          73/2    |  1   cot (x)|
      3     2/ 4\   73*cot    (x)*|- - - -------|
  12*x *acos \x /                 \  2      2   /
- --------------- + -----------------------------
       ________                 cot(x)           
      /      8                                   
    \/  1 - x
−12x3acos⁡2(x4)1−x8+73(−cot⁡2(x)2−12)cot⁡732(x)cot⁡(x)- \frac{12 x^{3} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} + \frac{73 \left(- \frac{\cot^{2}{\left(x \right)}}{2} - \frac{1}{2}\right) \cot^{\frac{73}{2}}{\left(x \right)}}{\cot{\left(x \right)}}
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Segunda derivada [src] 
                                                2                                                                 
                                   /       2   \     69/2          6     / 4\       10     2/ 4\       2     2/ 4\
      73/2    /       2   \   5183*\1 + cot (x)/ *cot    (x)   96*x *acos\x /   48*x  *acos \x /   36*x *acos \x /
73*cot    (x)*\1 + cot (x)/ + ------------------------------ - -------------- - ---------------- - ---------------
                                            4                           8                 3/2           ________  
                                                                  -1 + x          /     8\             /      8   
                                                                                  \1 - x /           \/  1 - x
−48x10acos⁡2(x4)(1−x8)32−96x6acos⁡(x4)x8−1−36x2acos⁡2(x4)1−x8+5183(cot⁡2(x)+1)2cot⁡692(x)4+73(cot⁡2(x)+1)cot⁡732(x)- \frac{48 x^{10} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{96 x^{6} \operatorname{acos}{\left(x^{4} \right)}}{x^{8} - 1} - \frac{36 x^{2} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} + \frac{5183 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{\frac{69}{2}}{\left(x \right)}}{4} + 73 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{\frac{73}{2}}{\left(x \right)}
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Tercera derivada [src] 
                                                                   3                                 2                                                                                                         
          9                                           /       2   \     67/2            /       2   \     71/2           5     / 4\        9     2/ 4\        17     2/ 4\            2/ 4\         13     / 4\
     384*x             75/2    /       2   \   357627*\1 + cot (x)/ *cot    (x)   15695*\1 + cot (x)/ *cot    (x)   864*x *acos\x /   624*x *acos \x /   576*x  *acos \x /   72*x*acos \x /   1152*x  *acos\x /
- ----------- - 146*cot    (x)*\1 + cot (x)/ - -------------------------------- - ------------------------------- - --------------- - ---------------- - ----------------- - -------------- + -----------------
          3/2                                                 8                                  2                            8                 3/2                 5/2          ________                  2   
  /     8\                                                                                                              -1 + x          /     8\            /     8\            /      8          /      8\    
  \1 - x /                                                                                                                              \1 - x /            \1 - x /          \/  1 - x           \-1 + x /
−576x17acos⁡2(x4)(1−x8)52+1152x13acos⁡(x4)(x8−1)2−624x9acos⁡2(x4)(1−x8)32−384x9(1−x8)32−864x5acos⁡(x4)x8−1−72xacos⁡2(x4)1−x8−357627(cot⁡2(x)+1)3cot⁡672(x)8−15695(cot⁡2(x)+1)2cot⁡712(x)2−146(cot⁡2(x)+1)cot⁡752(x)- \frac{576 x^{17} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{5}{2}}} + \frac{1152 x^{13} \operatorname{acos}{\left(x^{4} \right)}}{\left(x^{8} - 1\right)^{2}} - \frac{624 x^{9} \operatorname{acos}^{2}{\left(x^{4} \right)}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{384 x^{9}}{\left(1 - x^{8}\right)^{\frac{3}{2}}} - \frac{864 x^{5} \operatorname{acos}{\left(x^{4} \right)}}{x^{8} - 1} - \frac{72 x \operatorname{acos}^{2}{\left(x^{4} \right)}}{\sqrt{1 - x^{8}}} - \frac{357627 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \cot^{\frac{67}{2}}{\left(x \right)}}{8} - \frac{15695 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{\frac{71}{2}}{\left(x \right)}}{2} - 146 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{\frac{75}{2}}{\left(x \right)}
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Gráfico
Derivada de y=√cot^73x+arcos3(x^4)
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