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Derivada de la función/ y(x)=6cos(6arcctg(9arccos7x))

Derivada de y(x)=6cos(6arcctg(9arccos7x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
6*cos(6*acot(9*acos(7*x)))
6cos⁡(6acot⁡(9acos⁡(7x)))6 \cos{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)} 
6*cos(6*acot(9*acos(7*x)))
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  -2268*sin(6*acot(9*acos(7*x)))  
----------------------------------
   ___________                    
  /         2  /           2     \
\/  1 - 49*x  *\1 + 81*acos (7*x)/
−2268sin⁡(6acot⁡(9acos⁡(7x)))1−49x2(81acos⁡2(7x)+1)- \frac{2268 \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\sqrt{1 - 49 x^{2}} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)}
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Segunda derivada [src] 
      /  7*x*sin(6*acot(9*acos(7*x)))     54*cos(6*acot(9*acos(7*x)))      162*acos(7*x)*sin(6*acot(9*acos(7*x)))\
15876*|- ---------------------------- + -------------------------------- + --------------------------------------|
      |                    3/2          /           2     \ /         2\      /           2     \ /         2\   |
      |         /        2\             \1 + 81*acos (7*x)/*\-1 + 49*x /      \1 + 81*acos (7*x)/*\-1 + 49*x /   |
      \         \1 - 49*x /                                                                                      /
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                                                           2                                                      
                                                1 + 81*acos (7*x)
15876(−7xsin⁡(6acot⁡(9acos⁡(7x)))(1−49x2)32+162sin⁡(6acot⁡(9acos⁡(7x)))acos⁡(7x)(49x2−1)(81acos⁡2(7x)+1)+54cos⁡(6acot⁡(9acos⁡(7x)))(49x2−1)(81acos⁡2(7x)+1))81acos⁡2(7x)+1\frac{15876 \left(- \frac{7 x \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(1 - 49 x^{2}\right)^{\frac{3}{2}}} + \frac{162 \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)} \operatorname{acos}{\left(7 x \right)}}{\left(49 x^{2} - 1\right) \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)} + \frac{54 \cos{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(49 x^{2} - 1\right) \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)}\right)}{81 \operatorname{acos}^{2}{\left(7 x \right)} + 1}
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Tercera derivada [src] 
        /                                                                                                           2                                                                                                                     2                                                                          \
        |sin(6*acot(9*acos(7*x)))      2916*sin(6*acot(9*acos(7*x)))         162*sin(6*acot(9*acos(7*x)))      147*x *sin(6*acot(9*acos(7*x)))    1134*x*cos(6*acot(9*acos(7*x)))    26244*acos(7*x)*cos(6*acot(9*acos(7*x)))   52488*acos (7*x)*sin(6*acot(9*acos(7*x)))   3402*x*acos(7*x)*sin(6*acot(9*acos(7*x)))|
-111132*|------------------------ - ----------------------------------- - ---------------------------------- + ------------------------------- + --------------------------------- + ---------------------------------------- + ----------------------------------------- + -----------------------------------------|
        |                3/2                   3/2                    2              3/2                                           5/2                                           2                3/2                    2                    3/2                    2                                          2    |
        |     /        2\           /        2\    /           2     \    /        2\    /           2     \            /        2\              /           2     \ /         2\      /        2\    /           2     \          /        2\    /           2     \           /           2     \ /         2\     |
        \     \1 - 49*x /           \1 - 49*x /   *\1 + 81*acos (7*x)/    \1 - 49*x /   *\1 + 81*acos (7*x)/            \1 - 49*x /              \1 + 81*acos (7*x)/*\-1 + 49*x /      \1 - 49*x /   *\1 + 81*acos (7*x)/          \1 - 49*x /   *\1 + 81*acos (7*x)/           \1 + 81*acos (7*x)/*\-1 + 49*x /     /
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                                                                                                                                                             2                                                                                                                                                        
                                                                                                                                                  1 + 81*acos (7*x)
−111132(147x2sin⁡(6acot⁡(9acos⁡(7x)))(1−49x2)52+3402xsin⁡(6acot⁡(9acos⁡(7x)))acos⁡(7x)(49x2−1)2(81acos⁡2(7x)+1)+1134xcos⁡(6acot⁡(9acos⁡(7x)))(49x2−1)2(81acos⁡2(7x)+1)+sin⁡(6acot⁡(9acos⁡(7x)))(1−49x2)32−162sin⁡(6acot⁡(9acos⁡(7x)))(1−49x2)32(81acos⁡2(7x)+1)+52488sin⁡(6acot⁡(9acos⁡(7x)))acos⁡2(7x)(1−49x2)32(81acos⁡2(7x)+1)2−2916sin⁡(6acot⁡(9acos⁡(7x)))(1−49x2)32(81acos⁡2(7x)+1)2+26244cos⁡(6acot⁡(9acos⁡(7x)))acos⁡(7x)(1−49x2)32(81acos⁡2(7x)+1)2)81acos⁡2(7x)+1- \frac{111132 \left(\frac{147 x^{2} \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(1 - 49 x^{2}\right)^{\frac{5}{2}}} + \frac{3402 x \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)} \operatorname{acos}{\left(7 x \right)}}{\left(49 x^{2} - 1\right)^{2} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)} + \frac{1134 x \cos{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(49 x^{2} - 1\right)^{2} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)} + \frac{\sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(1 - 49 x^{2}\right)^{\frac{3}{2}}} - \frac{162 \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(1 - 49 x^{2}\right)^{\frac{3}{2}} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)} + \frac{52488 \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)} \operatorname{acos}^{2}{\left(7 x \right)}}{\left(1 - 49 x^{2}\right)^{\frac{3}{2}} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)^{2}} - \frac{2916 \sin{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)}}{\left(1 - 49 x^{2}\right)^{\frac{3}{2}} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)^{2}} + \frac{26244 \cos{\left(6 \operatorname{acot}{\left(9 \operatorname{acos}{\left(7 x \right)} \right)} \right)} \operatorname{acos}{\left(7 x \right)}}{\left(1 - 49 x^{2}\right)^{\frac{3}{2}} \left(81 \operatorname{acos}^{2}{\left(7 x \right)} + 1\right)^{2}}\right)}{81 \operatorname{acos}^{2}{\left(7 x \right)} + 1}
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