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

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de i*n*sin(x)
  • Derivada de i*n*x
  • Derivada de 3^-x Derivada de 3^-x
  • Derivada de y=6x Derivada de y=6x

  • Expresiones idénticas

  • y=arcsin^ tres (2x)*ctg(7x)^ cuatro
  • y es igual a arc seno de al cubo (2x) multiplicar por ctg(7x) en el grado 4
  • y es igual a arc seno de en el grado tres (2x) multiplicar por ctg(7x) en el grado cuatro
  • y=arcsin3(2x)*ctg(7x)4
  • y=arcsin32x*ctg7x4
  • y=arcsin³(2x)*ctg(7x)⁴
  • y=arcsin en el grado 3(2x)*ctg(7x) en el grado 4
  • y=arcsin^3(2x)ctg(7x)^4
  • y=arcsin3(2x)ctg(7x)4
  • y=arcsin32xctg7x4
  • y=arcsin^32xctg7x^4

  • Expresiones con funciones

  • arcsin
  • arcsin(lnx)
  • arcsin1/x
Derivada de la función/ sin^3/ tg(7x)/ arcsin/ y=arcsin^3(2x)*ctg(7x)^4

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

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

Gráfico:

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Solución

Ha introducido [src] 
    3         4     
asin (2*x)*cot (7*x)
cot⁡4(7x)asin⁡3(2x)\cot^{4}{\left(7 x \right)} \operatorname{asin}^{3}{\left(2 x \right)} 
asin(2*x)^3*cot(7*x)^4
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                                  2         4     
    3         3      /            2     \   6*asin (2*x)*cot (7*x)
asin (2*x)*cot (7*x)*\-28 - 28*cot (7*x)/ + ----------------------
                                                   __________     
                                                  /        2      
                                                \/  1 - 4*x
(−28cot⁡2(7x)−28)cot⁡3(7x)asin⁡3(2x)+6cot⁡4(7x)asin⁡2(2x)1−4x2\left(- 28 \cot^{2}{\left(7 x \right)} - 28\right) \cot^{3}{\left(7 x \right)} \operatorname{asin}^{3}{\left(2 x \right)} + \frac{6 \cot^{4}{\left(7 x \right)} \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}
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Segunda derivada [src] 
            /                                                                                                 /       2     \                   \          
     2      |     2      /      1        x*asin(2*x) \          2      /       2     \ /         2     \   84*\1 + cot (7*x)/*asin(2*x)*cot(7*x)|          
4*cot (7*x)*|6*cot (7*x)*|- --------- + -------------| + 49*asin (2*x)*\1 + cot (7*x)/*\3 + 5*cot (7*x)/ - -------------------------------------|*asin(2*x)
            |            |          2             3/2|                                                                    __________            |          
            |            |  -1 + 4*x    /       2\   |                                                                   /        2             |          
            \            \              \1 - 4*x /   /                                                                 \/  1 - 4*x              /
4(6(xasin⁡(2x)(1−4x2)32−14x2−1)cot⁡2(7x)+49(cot⁡2(7x)+1)(5cot⁡2(7x)+3)asin⁡2(2x)−84(cot⁡2(7x)+1)cot⁡(7x)asin⁡(2x)1−4x2)cot⁡2(7x)asin⁡(2x)4 \left(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^{2}{\left(7 x \right)} + 49 \left(\cot^{2}{\left(7 x \right)} + 1\right) \left(5 \cot^{2}{\left(7 x \right)} + 3\right) \operatorname{asin}^{2}{\left(2 x \right)} - \frac{84 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \cot^{2}{\left(7 x \right)} \operatorname{asin}{\left(2 x \right)}
Simplificar
Tercera derivada [src] 
  /            /                      2                              2     2     \                                  /                               2                               \                                                                                   2      /       2     \ /         2     \         \         
  |     3      |      2           asin (2*x)    12*x*asin(2*x)   12*x *asin (2*x)|           3      /       2     \ |     4          /       2     \          2      /       2     \|          2      /       2     \ /      1        x*asin(2*x) \             441*asin (2*x)*\1 + cot (7*x)/*\3 + 5*cot (7*x)/*cot(7*x)|         
8*|3*cot (7*x)*|------------- + ------------- + -------------- + ----------------| - 343*asin (2*x)*\1 + cot (7*x)/*\2*cot (7*x) + 3*\1 + cot (7*x)/  + 10*cot (7*x)*\1 + cot (7*x)// - 252*cot (7*x)*\1 + cot (7*x)/*|- --------- + -------------|*asin(2*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(−252(xasin⁡(2x)(1−4x2)32−14x2−1)(cot⁡2(7x)+1)cot⁡2(7x)asin⁡(2x)−343(cot⁡2(7x)+1)(3(cot⁡2(7x)+1)2+10(cot⁡2(7x)+1)cot⁡2(7x)+2cot⁡4(7x))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⁡3(7x)+441(cot⁡2(7x)+1)(5cot⁡2(7x)+3)cot⁡(7x)asin⁡2(2x)1−4x2)cot⁡(7x)8 \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) \cot^{2}{\left(7 x \right)} \operatorname{asin}{\left(2 x \right)} - 343 \left(\cot^{2}{\left(7 x \right)} + 1\right) \left(3 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} + 10 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot^{2}{\left(7 x \right)} + 2 \cot^{4}{\left(7 x \right)}\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^{3}{\left(7 x \right)} + \frac{441 \left(\cot^{2}{\left(7 x \right)} + 1\right) \left(5 \cot^{2}{\left(7 x \right)} + 3\right) \cot{\left(7 x \right)} \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \cot{\left(7 x \right)}
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Gráfico
Derivada de y=arcsin^3(2x)*ctg(7x)^4
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