Sr Examen

Otras calculadoras

y=(arcsin^34x)/sin(3x+1)
Derivada de la función/ arcsin/ sin^3/ sin(3x+1)/ y=(arcsin^34x)/sin(3x+1)

Derivada de y=(arcsin^34x)/sin(3x+1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     3      
 asin (4*x) 
------------
sin(3*x + 1)
asin⁡3(4x)sin⁡(3x+1)\frac{\operatorname{asin}^{3}{\left(4 x \right)}}{\sin{\left(3 x + 1 \right)}} 
asin(4*x)^3/sin(3*x + 1)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        3                                   2            
  3*asin (4*x)*cos(3*x + 1)          12*asin (4*x)       
- ------------------------- + ---------------------------
           2                     ___________             
        sin (3*x + 1)           /         2              
                              \/  1 - 16*x  *sin(3*x + 1)
−3cos⁡(3x+1)asin⁡3(4x)sin⁡2(3x+1)+12asin⁡2(4x)1−16x2sin⁡(3x+1)- \frac{3 \cos{\left(3 x + 1 \right)} \operatorname{asin}^{3}{\left(4 x \right)}}{\sin^{2}{\left(3 x + 1 \right)}} + \frac{12 \operatorname{asin}^{2}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \sin{\left(3 x + 1 \right)}}
Simplificar
Segunda derivada [src] 
  /                            /         2         \                                               \          
  |      32             2      |    2*cos (1 + 3*x)|   64*x*asin(4*x)    24*asin(4*x)*cos(1 + 3*x) |          
3*|- ---------- + 3*asin (4*x)*|1 + ---------------| + -------------- - ---------------------------|*asin(4*x)
  |           2                |        2          |              3/2      ___________             |          
  |  -1 + 16*x                 \     sin (1 + 3*x) /   /        2\        /         2              |          
  \                                                    \1 - 16*x /      \/  1 - 16*x  *sin(1 + 3*x)/          
--------------------------------------------------------------------------------------------------------------
                                                 sin(1 + 3*x)
3(64xasin⁡(4x)(1−16x2)32+3(1+2cos⁡2(3x+1)sin⁡2(3x+1))asin⁡2(4x)−3216x2−1−24cos⁡(3x+1)asin⁡(4x)1−16x2sin⁡(3x+1))asin⁡(4x)sin⁡(3x+1)\frac{3 \left(\frac{64 x \operatorname{asin}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + 3 \left(1 + \frac{2 \cos^{2}{\left(3 x + 1 \right)}}{\sin^{2}{\left(3 x + 1 \right)}}\right) \operatorname{asin}^{2}{\left(4 x \right)} - \frac{32}{16 x^{2} - 1} - \frac{24 \cos{\left(3 x + 1 \right)} \operatorname{asin}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \sin{\left(3 x + 1 \right)}}\right) \operatorname{asin}{\left(4 x \right)}}{\sin{\left(3 x + 1 \right)}}
Simplificar
Tercera derivada [src] 
  /                                                 /         2         \                                               /      1        2*x*asin(4*x) \                                       /         2         \             \
  |                                          2      |    2*cos (1 + 3*x)|                                           288*|- ---------- + --------------|*asin(4*x)*cos(1 + 3*x)         3      |    6*cos (1 + 3*x)|             |
  |                                  108*asin (4*x)*|1 + ---------------|                                               |           2              3/2|                          9*asin (4*x)*|5 + ---------------|*cos(1 + 3*x)|
  |                        2                        |        2          |                            2     2            |  -1 + 16*x    /        2\   |                                       |        2          |             |
  |     128         64*asin (4*x)                   \     sin (1 + 3*x) /   1536*x*asin(4*x)   3072*x *asin (4*x)       \               \1 - 16*x /   /                                       \     sin (1 + 3*x) /             |
3*|-------------- + -------------- + ------------------------------------ + ---------------- + ------------------ - ---------------------------------------------------------- - -----------------------------------------------|
  |           3/2              3/2                 ___________                           2                  5/2                            sin(1 + 3*x)                                            sin(1 + 3*x)                 |
  |/        2\      /        2\                   /         2                /         2\        /        2\                                                                                                                    |
  \\1 - 16*x /      \1 - 16*x /                 \/  1 - 16*x                 \-1 + 16*x /        \1 - 16*x /                                                                                                                    /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                           sin(1 + 3*x)
3(3072x2asin⁡2(4x)(1−16x2)52+1536xasin⁡(4x)(16x2−1)2−9(5+6cos⁡2(3x+1)sin⁡2(3x+1))cos⁡(3x+1)asin⁡3(4x)sin⁡(3x+1)−288(2xasin⁡(4x)(1−16x2)32−116x2−1)cos⁡(3x+1)asin⁡(4x)sin⁡(3x+1)+108(1+2cos⁡2(3x+1)sin⁡2(3x+1))asin⁡2(4x)1−16x2+64asin⁡2(4x)(1−16x2)32+128(1−16x2)32)sin⁡(3x+1)\frac{3 \left(\frac{3072 x^{2} \operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} + \frac{1536 x \operatorname{asin}{\left(4 x \right)}}{\left(16 x^{2} - 1\right)^{2}} - \frac{9 \left(5 + \frac{6 \cos^{2}{\left(3 x + 1 \right)}}{\sin^{2}{\left(3 x + 1 \right)}}\right) \cos{\left(3 x + 1 \right)} \operatorname{asin}^{3}{\left(4 x \right)}}{\sin{\left(3 x + 1 \right)}} - \frac{288 \left(\frac{2 x \operatorname{asin}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \cos{\left(3 x + 1 \right)} \operatorname{asin}{\left(4 x \right)}}{\sin{\left(3 x + 1 \right)}} + \frac{108 \left(1 + \frac{2 \cos^{2}{\left(3 x + 1 \right)}}{\sin^{2}{\left(3 x + 1 \right)}}\right) \operatorname{asin}^{2}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}}} + \frac{64 \operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{128}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right)}{\sin{\left(3 x + 1 \right)}}
Simplificar
Gráfico
Derivada de y=(arcsin^34x)/sin(3x+1)
    © Sr Examen – Калькулятор