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y=arcsin(√x-2)/√5x
Derivada de la función/ arcsin/ y=arcsin(√x-2)/√5x

Derivada de y=arcsin(√x-2)/√5x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
    /  ___    \
asin\\/ x  - 2/
---------------
      _____    
    \/ 5*x
asin⁡(x−2)5x\frac{\operatorname{asin}{\left(\sqrt{x} - 2 \right)}}{\sqrt{5 x}} 
asin(sqrt(x) - 2)/sqrt(5*x)
Gráfica
02468-8-6-4-2-10102-2
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Primera derivada [src] 
          /   ___ \                                   
          | \/ 5  |                                   
          |-------|                                   
          |    ___|                ___     /  ___    \
          \5*\/ x /              \/ 5 *asin\\/ x  - 2/
------------------------------ - ---------------------
            __________________              3/2       
           /                2           10*x          
    ___   /      /  ___    \                          
2*\/ x *\/   1 - \\/ x  - 2/
1551x2x1−(x−2)2−5asin⁡(x−2)10x32\frac{\frac{1}{5} \sqrt{5} \frac{1}{\sqrt{x}}}{2 \sqrt{x} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} - \frac{\sqrt{5} \operatorname{asin}{\left(\sqrt{x} - 2 \right)}}{10 x^{\frac{3}{2}}}
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Segunda derivada [src] 
      /                                                                        ___      \
      |                                                     1           -2 + \/ x       |
      |                                                    ---- + ----------------------|
      |                                                     3/2     /                 2\|
      |                                     /       ___\   x        |     /       ___\ ||
  ___ |              2                3*asin\-2 + \/ x /          x*\-1 + \-2 + \/ x / /|
\/ 5 *|- -------------------------- + ------------------ - -----------------------------|
      |         ___________________           5/2                    ___________________|
      |        /                 2           x                      /                 2 |
      |   2   /      /       ___\                            ___   /      /       ___\  |
      \  x *\/   1 - \-2 + \/ x /                          \/ x *\/   1 - \-2 + \/ x /  /
-----------------------------------------------------------------------------------------
                                            20
5(−2x21−(x−2)2−x−2x((x−2)2−1)+1x32x1−(x−2)2+3asin⁡(x−2)x52)20\frac{\sqrt{5} \left(- \frac{2}{x^{2} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} - \frac{\frac{\sqrt{x} - 2}{x \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{1}{x^{\frac{3}{2}}}}{\sqrt{x} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} + \frac{3 \operatorname{asin}{\left(\sqrt{x} - 2 \right)}}{x^{\frac{5}{2}}}\right)}{20}
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Tercera derivada [src] 
      /                                                                                                                                     2                                          \
      |                                                                                               /       ___\              /       ___\                                           |
      |                                                      3                 1                    3*\-2 + \/ x /            3*\-2 + \/ x /            /                    ___      \|
      |                                                     ---- - ------------------------- + ----------------------- + --------------------------     | 1           -2 + \/ x       ||
      |                                                      5/2        /                 2\      /                 2\                            2   3*|---- + ----------------------||
      |                                                     x       3/2 |     /       ___\ |    2 |     /       ___\ |        /                 2\      | 3/2     /                 2\||
      |         /       ___\                                       x   *\-1 + \-2 + \/ x / /   x *\-1 + \-2 + \/ x / /    3/2 |     /       ___\ |      |x        |     /       ___\ |||
  ___ |  15*asin\-2 + \/ x /               9                                                                             x   *\-1 + \-2 + \/ x / /      \       x*\-1 + \-2 + \/ x / //|
\/ 5 *|- ------------------- + -------------------------- + --------------------------------------------------------------------------------------- + ---------------------------------|
      |           7/2                 ___________________                                          ___________________                                            ___________________  |
      |          x                   /                 2                                          /                 2                                            /                 2   |
      |                         3   /      /       ___\                                    ___   /      /       ___\                                      3/2   /      /       ___\    |
      \                        x *\/   1 - \-2 + \/ x /                                  \/ x *\/   1 - \-2 + \/ x /                                     x   *\/   1 - \-2 + \/ x /    /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           40
5(9x31−(x−2)2+3(x−2)x2((x−2)2−1)+3(x−2)2x32((x−2)2−1)2−1x32((x−2)2−1)+3x52x1−(x−2)2+3(x−2x((x−2)2−1)+1x32)x321−(x−2)2−15asin⁡(x−2)x72)40\frac{\sqrt{5} \left(\frac{9}{x^{3} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} + \frac{\frac{3 \left(\sqrt{x} - 2\right)}{x^{2} \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{3 \left(\sqrt{x} - 2\right)^{2}}{x^{\frac{3}{2}} \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)^{2}} - \frac{1}{x^{\frac{3}{2}} \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{3}{x^{\frac{5}{2}}}}{\sqrt{x} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} + \frac{3 \left(\frac{\sqrt{x} - 2}{x \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{x^{\frac{3}{2}} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} - \frac{15 \operatorname{asin}{\left(\sqrt{x} - 2 \right)}}{x^{\frac{7}{2}}}\right)}{40}
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3-я производная [src] 
      /                                                                                                                                     2                                          \
      |                                                                                               /       ___\              /       ___\                                           |
      |                                                      3                 1                    3*\-2 + \/ x /            3*\-2 + \/ x /            /                    ___      \|
      |                                                     ---- - ------------------------- + ----------------------- + --------------------------     | 1           -2 + \/ x       ||
      |                                                      5/2        /                 2\      /                 2\                            2   3*|---- + ----------------------||
      |                                                     x       3/2 |     /       ___\ |    2 |     /       ___\ |        /                 2\      | 3/2     /                 2\||
      |         /       ___\                                       x   *\-1 + \-2 + \/ x / /   x *\-1 + \-2 + \/ x / /    3/2 |     /       ___\ |      |x        |     /       ___\ |||
  ___ |  15*asin\-2 + \/ x /               9                                                                             x   *\-1 + \-2 + \/ x / /      \       x*\-1 + \-2 + \/ x / //|
\/ 5 *|- ------------------- + -------------------------- + --------------------------------------------------------------------------------------- + ---------------------------------|
      |           7/2                 ___________________                                          ___________________                                            ___________________  |
      |          x                   /                 2                                          /                 2                                            /                 2   |
      |                         3   /      /       ___\                                    ___   /      /       ___\                                      3/2   /      /       ___\    |
      \                        x *\/   1 - \-2 + \/ x /                                  \/ x *\/   1 - \-2 + \/ x /                                     x   *\/   1 - \-2 + \/ x /    /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           40
5(9x31−(x−2)2+3(x−2)x2((x−2)2−1)+3(x−2)2x32((x−2)2−1)2−1x32((x−2)2−1)+3x52x1−(x−2)2+3(x−2x((x−2)2−1)+1x32)x321−(x−2)2−15asin⁡(x−2)x72)40\frac{\sqrt{5} \left(\frac{9}{x^{3} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} + \frac{\frac{3 \left(\sqrt{x} - 2\right)}{x^{2} \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{3 \left(\sqrt{x} - 2\right)^{2}}{x^{\frac{3}{2}} \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)^{2}} - \frac{1}{x^{\frac{3}{2}} \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{3}{x^{\frac{5}{2}}}}{\sqrt{x} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} + \frac{3 \left(\frac{\sqrt{x} - 2}{x \left(\left(\sqrt{x} - 2\right)^{2} - 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{x^{\frac{3}{2}} \sqrt{1 - \left(\sqrt{x} - 2\right)^{2}}} - \frac{15 \operatorname{asin}{\left(\sqrt{x} - 2 \right)}}{x^{\frac{7}{2}}}\right)}{40}
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Gráfico
Derivada de y=arcsin(√x-2)/√5x
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