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(x-2)^4*asin(5*x)^4
Derivada de la función/ (x-2)/ sin(5*x)/ (x-2)^4*asin(5*x)^4

Derivada de (x-2)^4*asin(5*x)^4

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

Gráfico:

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Solución

Ha introducido [src] 
       4     4     
(x - 2) *asin (5*x)
(x−2)4asin⁡4(5x)\left(x - 2\right)^{4} \operatorname{asin}^{4}{\left(5 x \right)} 
(x - 2)^4*asin(5*x)^4
Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
                                  4     3     
         3     4        20*(x - 2) *asin (5*x)
4*(x - 2) *asin (5*x) + ----------------------
                               ___________    
                              /         2     
                            \/  1 - 25*x
4(x−2)3asin⁡4(5x)+20(x−2)4asin⁡3(5x)1−25x24 \left(x - 2\right)^{3} \operatorname{asin}^{4}{\left(5 x \right)} + \frac{20 \left(x - 2\right)^{4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}
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Segunda derivada [src] 
          2     2      /      2                   2 /      3        5*x*asin(5*x) \   40*(-2 + x)*asin(5*x)\
4*(-2 + x) *asin (5*x)*|3*asin (5*x) + 25*(-2 + x) *|- ---------- + --------------| + ---------------------|
                       |                            |           2              3/2|          ___________   |
                       |                            |  -1 + 25*x    /        2\   |         /         2    |
                       \                            \               \1 - 25*x /   /       \/  1 - 25*x     /
4(x−2)2(25(x−2)2(5xasin⁡(5x)(1−25x2)32−325x2−1)+3asin⁡2(5x)+40(x−2)asin⁡(5x)1−25x2)asin⁡2(5x)4 \left(x - 2\right)^{2} \left(25 \left(x - 2\right)^{2} \left(\frac{5 x \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{3}{25 x^{2} - 1}\right) + 3 \operatorname{asin}^{2}{\left(5 x \right)} + \frac{40 \left(x - 2\right) \operatorname{asin}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}\right) \operatorname{asin}^{2}{\left(5 x \right)}
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Tercera derivada [src] 
           /                             /                       2                               2     2     \           2                                                                        \          
           |      3                    3 |      6            asin (5*x)     45*x*asin(5*x)   75*x *asin (5*x)|   180*asin (5*x)*(-2 + x)               2 /      3        5*x*asin(5*x) \          |          
4*(-2 + x)*|6*asin (5*x) + 125*(-2 + x) *|-------------- + -------------- + -------------- + ----------------| + ----------------------- + 300*(-2 + x) *|- ---------- + --------------|*asin(5*x)|*asin(5*x)
           |                             |           3/2              3/2               2                5/2 |           ___________                     |           2              3/2|          |          
           |                             |/        2\      /        2\      /         2\      /        2\    |          /         2                      |  -1 + 25*x    /        2\   |          |          
           \                             \\1 - 25*x /      \1 - 25*x /      \-1 + 25*x /      \1 - 25*x /    /        \/  1 - 25*x                       \               \1 - 25*x /   /          /
4(x−2)(125(x−2)3(75x2asin⁡2(5x)(1−25x2)52+45xasin⁡(5x)(25x2−1)2+asin⁡2(5x)(1−25x2)32+6(1−25x2)32)+300(x−2)2(5xasin⁡(5x)(1−25x2)32−325x2−1)asin⁡(5x)+6asin⁡3(5x)+180(x−2)asin⁡2(5x)1−25x2)asin⁡(5x)4 \left(x - 2\right) \left(125 \left(x - 2\right)^{3} \left(\frac{75 x^{2} \operatorname{asin}^{2}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{45 x \operatorname{asin}{\left(5 x \right)}}{\left(25 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}\right) + 300 \left(x - 2\right)^{2} \left(\frac{5 x \operatorname{asin}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{3}{25 x^{2} - 1}\right) \operatorname{asin}{\left(5 x \right)} + 6 \operatorname{asin}^{3}{\left(5 x \right)} + \frac{180 \left(x - 2\right) \operatorname{asin}^{2}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}\right) \operatorname{asin}{\left(5 x \right)}
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Gráfico
Derivada de (x-2)^4*asin(5*x)^4
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