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y=cos^3*4x*arcsin(√x)

Derivada de y=cos^3*4x*arcsin(√x)

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Solución

Ha introducido [src]
   3          /  ___\
cos (4)*x*asin\\/ x /
$$x \cos^{3}{\left(4 \right)} \operatorname{asin}{\left(\sqrt{x} \right)}$$
(cos(4)^3*x)*asin(sqrt(x))
Gráfica
Primera derivada [src]
                        ___    3   
   3        /  ___\   \/ x *cos (4)
cos (4)*asin\\/ x / + -------------
                           _______ 
                       2*\/ 1 - x  
$$\frac{\sqrt{x} \cos^{3}{\left(4 \right)}}{2 \sqrt{1 - x}} + \cos^{3}{\left(4 \right)} \operatorname{asin}{\left(\sqrt{x} \right)}$$
Segunda derivada [src]
        /          ___ /1     1   \\
        |        \/ x *|- + ------||
   3    |  1           \x   -1 + x/|
cos (4)*|----- - ------------------|
        |  ___           4         |
        \\/ x                      /
------------------------------------
               _______              
             \/ 1 - x               
$$\frac{\left(- \frac{\sqrt{x} \left(\frac{1}{x - 1} + \frac{1}{x}\right)}{4} + \frac{1}{\sqrt{x}}\right) \cos^{3}{\left(4 \right)}}{\sqrt{1 - x}}$$
Tercera derivada [src]
        /                                        /1     1   \\
        |                                      6*|- + ------||
   3    |  ___ /3        3           2     \     \x   -1 + x/|
cos (4)*|\/ x *|-- + --------- + ----------| - --------------|
        |      | 2           2   x*(-1 + x)|         ___     |
        \      \x    (-1 + x)              /       \/ x      /
--------------------------------------------------------------
                             _______                          
                         8*\/ 1 - x                           
$$\frac{\left(\sqrt{x} \left(\frac{3}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} + \frac{3}{x^{2}}\right) - \frac{6 \left(\frac{1}{x - 1} + \frac{1}{x}\right)}{\sqrt{x}}\right) \cos^{3}{\left(4 \right)}}{8 \sqrt{1 - x}}$$
Gráfico
Derivada de y=cos^3*4x*arcsin(√x)