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

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

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

Ha introducido [src] 
    3              
asin (2*x)*cot(7*x)
cot⁡(7x)asin⁡3(2x)\cot{\left(7 x \right)} \operatorname{asin}^{3}{\left(2 x \right)} 
asin(2*x)^3*cot(7*x)
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
                                      2              
    3      /          2     \   6*asin (2*x)*cot(7*x)
asin (2*x)*\-7 - 7*cot (7*x)/ + ---------------------
                                       __________    
                                      /        2     
                                    \/  1 - 4*x
(−7cot⁡2(7x)−7)asin⁡3(2x)+6cot⁡(7x)asin⁡2(2x)1−4x2\left(- 7 \cot^{2}{\left(7 x \right)} - 7\right) \operatorname{asin}^{3}{\left(2 x \right)} + \frac{6 \cot{\left(7 x \right)} \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}
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Segunda derivada [src] 
  /                                               /       2     \                                                   \          
  |   /      1        x*asin(2*x) \            42*\1 + cot (7*x)/*asin(2*x)          2      /       2     \         |          
2*|12*|- --------- + -------------|*cot(7*x) - ---------------------------- + 49*asin (2*x)*\1 + cot (7*x)/*cot(7*x)|*asin(2*x)
  |   |          2             3/2|                      __________                                                 |          
  |   |  -1 + 4*x    /       2\   |                     /        2                                                  |          
  \   \              \1 - 4*x /   /                   \/  1 - 4*x                                                   /
2(12(xasin⁡(2x)(1−4x2)32−14x2−1)cot⁡(7x)+49(cot⁡2(7x)+1)cot⁡(7x)asin⁡2(2x)−42(cot⁡2(7x)+1)asin⁡(2x)1−4x2)asin⁡(2x)2 \left(12 \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 \right)} + 49 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)} \operatorname{asin}^{2}{\left(2 x \right)} - \frac{42 \left(\cot^{2}{\left(7 x \right)} + 1\right) \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \operatorname{asin}{\left(2 x \right)}
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Tercera derivada [src] 
  /   /                      2                              2     2     \                                                                                                                                     2      /       2     \         \
  |   |      2           asin (2*x)    12*x*asin(2*x)   12*x *asin (2*x)|                    3      /       2     \ /         2     \       /       2     \ /      1        x*asin(2*x) \             882*asin (2*x)*\1 + cot (7*x)/*cot(7*x)|
2*|12*|------------- + ------------- + -------------- + ----------------|*cot(7*x) - 343*asin (2*x)*\1 + cot (7*x)/*\1 + 3*cot (7*x)/ - 252*\1 + cot (7*x)/*|- --------- + -------------|*asin(2*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               /
2(−252(xasin⁡(2x)(1−4x2)32−14x2−1)(cot⁡2(7x)+1)asin⁡(2x)−343(cot⁡2(7x)+1)(3cot⁡2(7x)+1)asin⁡3(2x)+12(12x2asin⁡2(2x)(1−4x2)52+12xasin⁡(2x)(4x2−1)2+asin⁡2(2x)(1−4x2)32+2(1−4x2)32)cot⁡(7x)+882(cot⁡2(7x)+1)cot⁡(7x)asin⁡2(2x)1−4x2)2 \left(- 252 \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 \right)} + 1\right) \operatorname{asin}{\left(2 x \right)} - 343 \left(\cot^{2}{\left(7 x \right)} + 1\right) \left(3 \cot^{2}{\left(7 x \right)} + 1\right) \operatorname{asin}^{3}{\left(2 x \right)} + 12 \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 \right)} + \frac{882 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)} \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right)
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Gráfico
Derivada de y=asin^3(2x)*ctg(7x)
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