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y=4cos(arcsin((x/2)^1/3))
Derivada de la función/ arcsin/ (x/2)/ y=4cos(arcsin((x/2)^1/3))

Derivada de y=4cos(arcsin((x/2)^1/3))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     /    /    ___\\
     |    |   / x ||
4*cos|asin|3 /  - ||
     \    \\/   2 //
4cos⁡(asin⁡(x23))4 \cos{\left(\operatorname{asin}{\left(\sqrt[3]{\frac{x}{2}} \right)} \right)} 
4*cos(asin((x/2)^(1/3)))
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
              3 ___          
           -2*\/ 2           
-----------------------------
             ________________
            /     3 ___  2/3 
  3 ___    /      \/ 2 *x    
3*\/ x *  /   1 - ---------- 
        \/            2
−2233x3−23x232+1- \frac{2 \sqrt[3]{2}}{3 \sqrt[3]{x} \sqrt{- \frac{\sqrt[3]{2} x^{\frac{2}{3}}}{2} + 1}}
Simplificar
Segunda derivada [src] 
        /            3 ___     \
  3 ___ | 1          \/ 2      |
2*\/ 2 *|---- + ---------------|
        | 2/3        3 ___  2/3|
        \x      -2 + \/ 2 *x   /
--------------------------------
              ________________  
             /     3 ___  2/3   
     2/3    /      \/ 2 *x      
  9*x   *  /   1 - ----------   
         \/            2
223(2323x23−2+1x23)9x23−23x232+1\frac{2 \sqrt[3]{2} \left(\frac{\sqrt[3]{2}}{\sqrt[3]{2} x^{\frac{2}{3}} - 2} + \frac{1}{x^{\frac{2}{3}}}\right)}{9 x^{\frac{2}{3}} \sqrt{- \frac{\sqrt[3]{2} x^{\frac{2}{3}}}{2} + 1}}
Simplificar
Tercera derivada [src] 
   /  3 ___                                     2/3        \
   |4*\/ 2             6                     3*2           |
-2*|------- + -------------------- + ----------------------|
   |   7/3                       2    5/3 /     3 ___  2/3\|
   |  x         /     3 ___  2/3\    x   *\-2 + \/ 2 *x   /|
   \          x*\-2 + \/ 2 *x   /                          /
------------------------------------------------------------
                          ________________                  
                         /     3 ___  2/3                   
                        /      \/ 2 *x                      
                  27*  /   1 - ----------                   
                     \/            2
−2(6x(23x23−2)2+3⋅223x53(23x23−2)+423x73)27−23x232+1- \frac{2 \left(\frac{6}{x \left(\sqrt[3]{2} x^{\frac{2}{3}} - 2\right)^{2}} + \frac{3 \cdot 2^{\frac{2}{3}}}{x^{\frac{5}{3}} \left(\sqrt[3]{2} x^{\frac{2}{3}} - 2\right)} + \frac{4 \sqrt[3]{2}}{x^{\frac{7}{3}}}\right)}{27 \sqrt{- \frac{\sqrt[3]{2} x^{\frac{2}{3}}}{2} + 1}}
Simplificar
3-я производная [src] 
   /  3 ___                                     2/3        \
   |4*\/ 2             6                     3*2           |
-2*|------- + -------------------- + ----------------------|
   |   7/3                       2    5/3 /     3 ___  2/3\|
   |  x         /     3 ___  2/3\    x   *\-2 + \/ 2 *x   /|
   \          x*\-2 + \/ 2 *x   /                          /
------------------------------------------------------------
                          ________________                  
                         /     3 ___  2/3                   
                        /      \/ 2 *x                      
                  27*  /   1 - ----------                   
                     \/            2
−2(6x(23x23−2)2+3⋅223x53(23x23−2)+423x73)27−23x232+1- \frac{2 \left(\frac{6}{x \left(\sqrt[3]{2} x^{\frac{2}{3}} - 2\right)^{2}} + \frac{3 \cdot 2^{\frac{2}{3}}}{x^{\frac{5}{3}} \left(\sqrt[3]{2} x^{\frac{2}{3}} - 2\right)} + \frac{4 \sqrt[3]{2}}{x^{\frac{7}{3}}}\right)}{27 \sqrt{- \frac{\sqrt[3]{2} x^{\frac{2}{3}}}{2} + 1}}
Simplificar
Gráfico
Derivada de y=4cos(arcsin((x/2)^1/3))
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