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sqrt(-16x^2-8x)*arcsin(4x+1)
Derivada de la función/ sqrt(-16x^2-8x)*arcsin(4x+1)

Derivada de sqrt(-16x^2-8x)*arcsin(4x+1)

Función f() - derivada -er orden en el punto
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Ha introducido [src] 
   _______________              
  /       2                     
\/  - 16*x  - 8*x *asin(4*x + 1)
−16x2−8xasin⁡(4x+1)\sqrt{- 16 x^{2} - 8 x} \operatorname{asin}{\left(4 x + 1 \right)} 
sqrt(-16*x^2 - 8*x)*asin(4*x + 1)
Gráfica
02468-8-6-4-2-10105-5
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Primera derivada [src] 
     _______________                            
    /       2                                   
4*\/  - 16*x  - 8*x    (-4 - 16*x)*asin(4*x + 1)
-------------------- + -------------------------
   ________________           _______________   
  /              2           /       2          
\/  1 - (4*x + 1)          \/  - 16*x  - 8*x
(−16x−4)asin⁡(4x+1)−16x2−8x+4−16x2−8x1−(4x+1)2\frac{\left(- 16 x - 4\right) \operatorname{asin}{\left(4 x + 1 \right)}}{\sqrt{- 16 x^{2} - 8 x}} + \frac{4 \sqrt{- 16 x^{2} - 8 x}}{\sqrt{1 - \left(4 x + 1\right)^{2}}}
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Segunda derivada [src] 
      /                                                                         /              2\              \
      |                                                                         |     (1 + 4*x) |              |
      |                                              ______________             |8 - -----------|*asin(1 + 4*x)|
  ___ |              8*(1 + 4*x)                32*\/ -x*(1 + 2*x) *(1 + 4*x)   \    x*(1 + 2*x)/              |
\/ 2 *|- ------------------------------------ + ----------------------------- - -------------------------------|
      |                      ________________                        3/2                   ______________      |
      |    ______________   /              2         /             2\                  2*\/ -x*(1 + 2*x)       |
      \  \/ -x*(1 + 2*x) *\/  1 - (1 + 4*x)          \1 - (1 + 4*x) /                                          /
2(32−x(2x+1)(4x+1)(1−(4x+1)2)32−(8−(4x+1)2x(2x+1))asin⁡(4x+1)2−x(2x+1)−8(4x+1)−x(2x+1)1−(4x+1)2)\sqrt{2} \left(\frac{32 \sqrt{- x \left(2 x + 1\right)} \left(4 x + 1\right)}{\left(1 - \left(4 x + 1\right)^{2}\right)^{\frac{3}{2}}} - \frac{\left(8 - \frac{\left(4 x + 1\right)^{2}}{x \left(2 x + 1\right)}\right) \operatorname{asin}{\left(4 x + 1 \right)}}{2 \sqrt{- x \left(2 x + 1\right)}} - \frac{8 \left(4 x + 1\right)}{\sqrt{- x \left(2 x + 1\right)} \sqrt{1 - \left(4 x + 1\right)^{2}}}\right)
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Tercera derivada [src] 
       /                                                                                                   /                  2 \                                              \
       |          /              2\                                                         ______________ |       3*(1 + 4*x)  |               /              2\              |
       |          |     (1 + 4*x) |                                                   128*\/ -x*(1 + 2*x) *|-1 + ---------------|               |     (1 + 4*x) |              |
       |        6*|8 - -----------|                                   2                                    |                   2|   3*(1 + 4*x)*|8 - -----------|*asin(1 + 4*x)|
   ___ |          \    x*(1 + 2*x)/                       48*(1 + 4*x)                                     \     -1 + (1 + 4*x) /               \    x*(1 + 2*x)/              |
-\/ 2 *|------------------------------------ + ------------------------------------ + ------------------------------------------- + -------------------------------------------|
       |                    ________________                                    3/2                               3/2                                           3/2            |
       |  ______________   /              2      ______________ /             2\                  /             2\                              4*(-x*(1 + 2*x))               |
       \\/ -x*(1 + 2*x) *\/  1 - (1 + 4*x)     \/ -x*(1 + 2*x) *\1 - (1 + 4*x) /                  \1 - (1 + 4*x) /                                                             /
−2(128−x(2x+1)(3(4x+1)2(4x+1)2−1−1)(1−(4x+1)2)32+6(8−(4x+1)2x(2x+1))−x(2x+1)1−(4x+1)2+48(4x+1)2−x(2x+1)(1−(4x+1)2)32+3(8−(4x+1)2x(2x+1))(4x+1)asin⁡(4x+1)4(−x(2x+1))32)- \sqrt{2} \left(\frac{128 \sqrt{- x \left(2 x + 1\right)} \left(\frac{3 \left(4 x + 1\right)^{2}}{\left(4 x + 1\right)^{2} - 1} - 1\right)}{\left(1 - \left(4 x + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{6 \left(8 - \frac{\left(4 x + 1\right)^{2}}{x \left(2 x + 1\right)}\right)}{\sqrt{- x \left(2 x + 1\right)} \sqrt{1 - \left(4 x + 1\right)^{2}}} + \frac{48 \left(4 x + 1\right)^{2}}{\sqrt{- x \left(2 x + 1\right)} \left(1 - \left(4 x + 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(8 - \frac{\left(4 x + 1\right)^{2}}{x \left(2 x + 1\right)}\right) \left(4 x + 1\right) \operatorname{asin}{\left(4 x + 1 \right)}}{4 \left(- x \left(2 x + 1\right)\right)^{\frac{3}{2}}}\right)
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Gráfico
Derivada de sqrt(-16x^2-8x)*arcsin(4x+1)
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