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x*(x-8)^(1/4)+4arcsin(x/2)

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

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

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Solución

Ha introducido [src]
  4 _______         /x\
x*\/ x - 8  + 4*asin|-|
                    \2/
$$x \sqrt[4]{x - 8} + 4 \operatorname{asin}{\left(\frac{x}{2} \right)}$$
x*(x - 8)^(1/4) + 4*asin(x/2)
Gráfica
Primera derivada [src]
4 _______         2              x      
\/ x - 8  + ------------- + ------------
                 ________            3/4
                /      2    4*(x - 8)   
               /      x                 
              /   1 - --                
            \/        4                 
$$\frac{x}{4 \left(x - 8\right)^{\frac{3}{4}}} + \sqrt[4]{x - 8} + \frac{2}{\sqrt{1 - \frac{x^{2}}{4}}}$$
Segunda derivada [src]
     8            3*x           8*x    
----------- - ----------- + -----------
        3/4           7/4           3/2
(-8 + x)      (-8 + x)      /     2\   
                            |    x |   
                            |1 - --|   
                            \    4 /   
---------------------------------------
                   16                  
$$\frac{- \frac{3 x}{\left(x - 8\right)^{\frac{7}{4}}} + \frac{8 x}{\left(1 - \frac{x^{2}}{4}\right)^{\frac{3}{2}}} + \frac{8}{\left(x - 8\right)^{\frac{3}{4}}}}{16}$$
Tercera derivada [src]
                                                    2   
       36            32           21*x          24*x    
- ----------- + ----------- + ------------ + -----------
          7/4           3/2           11/4           5/2
  (-8 + x)      /     2\      (-8 + x)       /     2\   
                |    x |                     |    x |   
                |1 - --|                     |1 - --|   
                \    4 /                     \    4 /   
--------------------------------------------------------
                           64                           
$$\frac{\frac{24 x^{2}}{\left(1 - \frac{x^{2}}{4}\right)^{\frac{5}{2}}} + \frac{21 x}{\left(x - 8\right)^{\frac{11}{4}}} - \frac{36}{\left(x - 8\right)^{\frac{7}{4}}} + \frac{32}{\left(1 - \frac{x^{2}}{4}\right)^{\frac{3}{2}}}}{64}$$
Gráfico
Derivada de x*(x-8)^(1/4)+4arcsin(x/2)