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y=sqrt(x^2-1)+arccos^7((x^3)-5)
Derivada de la función/ y=sqrt(x^2-1)+arccos^7((x^3)-5)

Derivada de y=sqrt(x^2-1)+arccos^7((x^3)-5)

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

Gráfico:

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Solución

Ha introducido [src] 
   ________                
  /  2            7/ 3    \
\/  x  - 1  + acos \x  - 5/
x2−1+acos⁡7(x3−5)\sqrt{x^{2} - 1} + \operatorname{acos}^{7}{\left(x^{3} - 5 \right)} 
sqrt(x^2 - 1) + acos(x^3 - 5)^7
Gráfica
02468-8-6-4-2-1010-10001000
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Primera derivada [src] 
                  2     6/ 3    \
     x        21*x *acos \x  - 5/
----------- - -------------------
   ________       _______________
  /  2           /             2 
\/  x  - 1      /      / 3    \  
              \/   1 - \x  - 5/
−21x2acos⁡6(x3−5)1−(x3−5)2+xx2−1- \frac{21 x^{2} \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\sqrt{1 - \left(x^{3} - 5\right)^{2}}} + \frac{x}{\sqrt{x^{2} - 1}}
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Segunda derivada [src] 
                     2             4     5/      3\            6/      3\        4     6/      3\ /      3\
     1              x         378*x *acos \-5 + x /   42*x*acos \-5 + x /    63*x *acos \-5 + x /*\-5 + x /
------------ - ------------ - --------------------- - -------------------- - ------------------------------
   _________            3/2                    2          ________________                        3/2      
  /       2    /      2\              /      3\          /              2         /             2\         
\/  -1 + x     \-1 + x /         -1 + \-5 + x /         /      /      3\          |    /      3\ |         
                                                      \/   1 - \-5 + x /          \1 - \-5 + x / /
−378x4acos⁡5(x3−5)(x3−5)2−1−63x4(x3−5)acos⁡6(x3−5)(1−(x3−5)2)32−x2(x2−1)32−42xacos⁡6(x3−5)1−(x3−5)2+1x2−1- \frac{378 x^{4} \operatorname{acos}^{5}{\left(x^{3} - 5 \right)}}{\left(x^{3} - 5\right)^{2} - 1} - \frac{63 x^{4} \left(x^{3} - 5\right) \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\left(1 - \left(x^{3} - 5\right)^{2}\right)^{\frac{3}{2}}} - \frac{x^{2}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{42 x \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\sqrt{1 - \left(x^{3} - 5\right)^{2}}} + \frac{1}{\sqrt{x^{2} - 1}}
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Tercera derivada [src] 
  /                                                                                                                                             2                                                                                    \
  |      3                               6/      3\           6     4/      3\        3     5/      3\       6     6/      3\        6 /      3\      6/      3\        3     6/      3\ /      3\         6     5/      3\ /      3\|
  |     x              x          14*acos \-5 + x /     1890*x *acos \-5 + x /   756*x *acos \-5 + x /   63*x *acos \-5 + x /   189*x *\-5 + x / *acos \-5 + x /   126*x *acos \-5 + x /*\-5 + x /   1134*x *acos \-5 + x /*\-5 + x /|
3*|------------ - ------------ - -------------------- - ---------------------- - --------------------- - -------------------- - -------------------------------- - ------------------------------- + --------------------------------|
  |         5/2            3/2       ________________                    3/2                      2                      3/2                          5/2                                3/2                                 2       |
  |/      2\      /      2\         /              2     /             2\                /      3\       /             2\             /             2\                   /             2\                   /              2\        |
  |\-1 + x /      \-1 + x /        /      /      3\      |    /      3\ |           -1 + \-5 + x /       |    /      3\ |             |    /      3\ |                   |    /      3\ |                   |     /      3\ |        |
  \                              \/   1 - \-5 + x /      \1 - \-5 + x / /                                \1 - \-5 + x / /             \1 - \-5 + x / /                   \1 - \-5 + x / /                   \-1 + \-5 + x / /        /
3(1134x6(x3−5)acos⁡5(x3−5)((x3−5)2−1)2−63x6acos⁡6(x3−5)(1−(x3−5)2)32−1890x6acos⁡4(x3−5)(1−(x3−5)2)32−189x6(x3−5)2acos⁡6(x3−5)(1−(x3−5)2)52−756x3acos⁡5(x3−5)(x3−5)2−1+x3(x2−1)52−126x3(x3−5)acos⁡6(x3−5)(1−(x3−5)2)32−x(x2−1)32−14acos⁡6(x3−5)1−(x3−5)2)3 \left(\frac{1134 x^{6} \left(x^{3} - 5\right) \operatorname{acos}^{5}{\left(x^{3} - 5 \right)}}{\left(\left(x^{3} - 5\right)^{2} - 1\right)^{2}} - \frac{63 x^{6} \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\left(1 - \left(x^{3} - 5\right)^{2}\right)^{\frac{3}{2}}} - \frac{1890 x^{6} \operatorname{acos}^{4}{\left(x^{3} - 5 \right)}}{\left(1 - \left(x^{3} - 5\right)^{2}\right)^{\frac{3}{2}}} - \frac{189 x^{6} \left(x^{3} - 5\right)^{2} \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\left(1 - \left(x^{3} - 5\right)^{2}\right)^{\frac{5}{2}}} - \frac{756 x^{3} \operatorname{acos}^{5}{\left(x^{3} - 5 \right)}}{\left(x^{3} - 5\right)^{2} - 1} + \frac{x^{3}}{\left(x^{2} - 1\right)^{\frac{5}{2}}} - \frac{126 x^{3} \left(x^{3} - 5\right) \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\left(1 - \left(x^{3} - 5\right)^{2}\right)^{\frac{3}{2}}} - \frac{x}{\left(x^{2} - 1\right)^{\frac{3}{2}}} - \frac{14 \operatorname{acos}^{6}{\left(x^{3} - 5 \right)}}{\sqrt{1 - \left(x^{3} - 5\right)^{2}}}\right)
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Gráfico
Derivada de y=sqrt(x^2-1)+arccos^7((x^3)-5)
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