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z=arcsin(4t^2-2t)
Derivada de la función/ arcsin/ z=arcsin(4t^2-2t)

Derivada de z=arcsin(4t^2-2t)

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Solución

Ha introducido [src] 
    /   2      \
asin\4*t  - 2*t/
asin⁡(4t2−2t)\operatorname{asin}{\left(4 t^{2} - 2 t \right)} 
asin(4*t^2 - 2*t)
Gráfica
02468-8-6-4-2-1010-2525
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Trazar el gráfico f'(x)
Primera derivada [src] 
        -2 + 8*t       
-----------------------
    ___________________
   /                 2 
  /      /   2      \  
\/   1 - \4*t  - 2*t/
8t−21−(4t2−2t)2\frac{8 t - 2}{\sqrt{1 - \left(4 t^{2} - 2 t\right)^{2}}}
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Segunda derivada [src] 
  /                2           \
  |    t*(-1 + 4*t) *(-1 + 2*t)|
8*|1 + ------------------------|
  |             2           2  |
  \      1 - 4*t *(-1 + 2*t)   /
--------------------------------
      ______________________    
     /        2           2     
   \/  1 - 4*t *(-1 + 2*t)
8(t(2t−1)(4t−1)2−4t2(2t−1)2+1+1)−4t2(2t−1)2+1\frac{8 \left(\frac{t \left(2 t - 1\right) \left(4 t - 1\right)^{2}}{- 4 t^{2} \left(2 t - 1\right)^{2} + 1} + 1\right)}{\sqrt{- 4 t^{2} \left(2 t - 1\right)^{2} + 1}}
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Tercera derivada [src] 
             /                                    2           2           2\
             |          2                     12*t *(-1 + 2*t) *(-1 + 4*t) |
8*(-1 + 4*t)*|(-1 + 4*t)  + 12*t*(-1 + 2*t) + -----------------------------|
             |                                            2           2    |
             \                                     1 - 4*t *(-1 + 2*t)     /
----------------------------------------------------------------------------
                                               3/2                          
                         /       2           2\                             
                         \1 - 4*t *(-1 + 2*t) /
8(4t−1)(12t2(2t−1)2(4t−1)2−4t2(2t−1)2+1+12t(2t−1)+(4t−1)2)(−4t2(2t−1)2+1)32\frac{8 \left(4 t - 1\right) \left(\frac{12 t^{2} \left(2 t - 1\right)^{2} \left(4 t - 1\right)^{2}}{- 4 t^{2} \left(2 t - 1\right)^{2} + 1} + 12 t \left(2 t - 1\right) + \left(4 t - 1\right)^{2}\right)}{\left(- 4 t^{2} \left(2 t - 1\right)^{2} + 1\right)^{\frac{3}{2}}}
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Gráfico
Derivada de z=arcsin(4t^2-2t)
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