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y=arcsin^3(2x)*ctg(7(x^4))
Derivada de la función/ (x^4)/ sin^3/ arcsin/ y=arcsin^3(2x)*ctg(7(x^4))

Derivada de y=arcsin^3(2x)*ctg(7(x^4))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
    3         /   4\
asin (2*x)*cot\7*x /
cot⁡(7x4)asin⁡3(2x)\cot{\left(7 x^{4} \right)} \operatorname{asin}^{3}{\left(2 x \right)} 
asin(2*x)^3*cot(7*x^4)
Gráfica
02468-8-6-4-2-1010-200100
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Primera derivada [src] 
      2         /   4\                                     
6*asin (2*x)*cot\7*x /       3     3      /        2/   4\\
---------------------- + 28*x *asin (2*x)*\-1 - cot \7*x //
       __________                                          
      /        2                                           
    \/  1 - 4*x
28x3(−cot⁡2(7x4)−1)asin⁡3(2x)+6cot⁡(7x4)asin⁡2(2x)1−4x228 x^{3} \left(- \cot^{2}{\left(7 x^{4} \right)} - 1\right) \operatorname{asin}^{3}{\left(2 x \right)} + \frac{6 \cot{\left(7 x^{4} \right)} \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}
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Segunda derivada [src] 
  /                                                3 /       2/   4\\                                                                    \          
  |  /      1        x*asin(2*x) \    /   4\   84*x *\1 + cot \7*x //*asin(2*x)      2     2      /       2/   4\\ /         4    /   4\\|          
4*|6*|- --------- + -------------|*cot\7*x / - -------------------------------- + 7*x *asin (2*x)*\1 + cot \7*x //*\-3 + 56*x *cot\7*x //|*asin(2*x)
  |  |          2             3/2|                         __________                                                                    |          
  |  |  -1 + 4*x    /       2\   |                        /        2                                                                     |          
  \  \              \1 - 4*x /   /                      \/  1 - 4*x                                                                      /
4(−84x3(cot⁡2(7x4)+1)asin⁡(2x)1−4x2+7x2(56x4cot⁡(7x4)−3)(cot⁡2(7x4)+1)asin⁡2(2x)+6(xasin⁡(2x)(1−4x2)32−14x2−1)cot⁡(7x4))asin⁡(2x)4 \left(- \frac{84 x^{3} \left(\cot^{2}{\left(7 x^{4} \right)} + 1\right) \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}} + 7 x^{2} \left(56 x^{4} \cot{\left(7 x^{4} \right)} - 3\right) \left(\cot^{2}{\left(7 x^{4} \right)} + 1\right) \operatorname{asin}^{2}{\left(2 x \right)} + 6 \left(\frac{x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \cot{\left(7 x^{4} \right)}\right) \operatorname{asin}{\left(2 x \right)}
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Tercera derivada [src] 
  /  /                      2                              2     2     \                                                                                                                                                                                           2     2      /       2/   4\\ /         4    /   4\\\
  |  |      2           asin (2*x)    12*x*asin(2*x)   12*x *asin (2*x)|    /   4\        3 /       2/   4\\ /      1        x*asin(2*x) \                     3      /       2/   4\\ /         4    /   4\        8 /       2/   4\\         8    2/   4\\   63*x *asin (2*x)*\1 + cot \7*x //*\-3 + 56*x *cot\7*x //|
8*|3*|------------- + ------------- + -------------- + ----------------|*cot\7*x / - 252*x *\1 + cot \7*x //*|- --------- + -------------|*asin(2*x) - 7*x*asin (2*x)*\1 + cot \7*x //*\3 - 252*x *cot\7*x / + 784*x *\1 + cot \7*x // + 1568*x *cot \7*x // + --------------------------------------------------------|
  |  |          3/2             3/2               2               5/2  |                                     |          2             3/2|                                                                                                                                             __________                      |
  |  |/       2\      /       2\       /        2\      /       2\     |                                     |  -1 + 4*x    /       2\   |                                                                                                                                            /        2                       |
  \  \\1 - 4*x /      \1 - 4*x /       \-1 + 4*x /      \1 - 4*x /     /                                     \              \1 - 4*x /   /                                                                                                                                          \/  1 - 4*x                        /
8(−252x3(xasin⁡(2x)(1−4x2)32−14x2−1)(cot⁡2(7x4)+1)asin⁡(2x)+63x2(56x4cot⁡(7x4)−3)(cot⁡2(7x4)+1)asin⁡2(2x)1−4x2−7x(cot⁡2(7x4)+1)(784x8(cot⁡2(7x4)+1)+1568x8cot⁡2(7x4)−252x4cot⁡(7x4)+3)asin⁡3(2x)+3(12x2asin⁡2(2x)(1−4x2)52+12xasin⁡(2x)(4x2−1)2+asin⁡2(2x)(1−4x2)32+2(1−4x2)32)cot⁡(7x4))8 \left(- 252 x^{3} \left(\frac{x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \left(\cot^{2}{\left(7 x^{4} \right)} + 1\right) \operatorname{asin}{\left(2 x \right)} + \frac{63 x^{2} \left(56 x^{4} \cot{\left(7 x^{4} \right)} - 3\right) \left(\cot^{2}{\left(7 x^{4} \right)} + 1\right) \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}} - 7 x \left(\cot^{2}{\left(7 x^{4} \right)} + 1\right) \left(784 x^{8} \left(\cot^{2}{\left(7 x^{4} \right)} + 1\right) + 1568 x^{8} \cot^{2}{\left(7 x^{4} \right)} - 252 x^{4} \cot{\left(7 x^{4} \right)} + 3\right) \operatorname{asin}^{3}{\left(2 x \right)} + 3 \left(\frac{12 x^{2} \operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right) \cot{\left(7 x^{4} \right)}\right)
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Gráfico
Derivada de y=arcsin^3(2x)*ctg(7(x^4))
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