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y= tres ^arccos^ dos (tg4x)
y es igual a 3 en el grado arc coseno de al cuadrado (tg4x)
y es igual a tres en el grado arc coseno de en el grado dos (tg4x)
y=3arccos2(tg4x)
y=3arccos2tg4x
y=3^arccos²(tg4x)
y=3 en el grado arccos en el grado 2(tg4x)
y=3^arccos^2tg4x
Expresiones con funciones
arccos
arccos(1/x)
arccos4
arccos(2^x)
arccos^2(x)

Derivada de la función/ cos^2/ arccos/ y=3^arccos^2(tg4x)

Derivada de y=3^arccos^2(tg4x)

Solución

Ha introducido [src]

     2          
 acos (tan(4*x))
3

3^{\operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}}

3^(acos(tan(4*x))^2)

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

        2                                                  
    acos (tan(4*x)) /         2     \                      
-2*3               *\4 + 4*tan (4*x)/*acos(tan(4*x))*log(3)
-----------------------------------------------------------
                        _______________                    
                       /        2                          
                     \/  1 - tan (4*x)

- \frac{2 \cdot 3^{\operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}} \left(4 \tan^{2}{\left(4 x \right)} + 4\right) \log{\left(3 \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\sqrt{1 - \tan^{2}{\left(4 x \right)}}}

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Segunda derivada [src]

         2                           /       2                                     /       2     \                                 2           /       2     \       \       
     acos (tan(4*x)) /       2     \ |1 + tan (4*x)    2*acos(tan(4*x))*tan(4*x)   \1 + tan (4*x)/*acos(tan(4*x))*tan(4*x)   2*acos (tan(4*x))*\1 + tan (4*x)/*log(3)|       
-32*3               *\1 + tan (4*x)/*|-------------- + ------------------------- + --------------------------------------- + ----------------------------------------|*log(3)
                                     |        2               _______________                                3/2                                  2                  |       
                                     |-1 + tan (4*x)         /        2                       /       2     \                             -1 + tan (4*x)             |       
                                     \                     \/  1 - tan (4*x)                  \1 - tan (4*x)/                                                        /

- 32 \cdot 3^{\operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}} \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(\frac{2 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(3 \right)} \operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}}{\tan^{2}{\left(4 x \right)} - 1} + \frac{\tan^{2}{\left(4 x \right)} + 1}{\tan^{2}{\left(4 x \right)} - 1} + \frac{2 \tan{\left(4 x \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\sqrt{1 - \tan^{2}{\left(4 x \right)}}} + \frac{\left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\left(1 - \tan^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}}\right) \log{\left(3 \right)}

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Tercera derivada [src]

                                     /                 2                                                                                                                                2                             2                                                                                       2                                            2                                                                                                  2                                \       
         2                           |  /       2     \                     /       2     \                 2                         /       2     \                    /       2     \               /       2     \                               2      /       2     \                    /       2     \      3              2        /       2     \     2                              2           /       2     \                     /       2     \      2                          |       
     acos (tan(4*x)) /       2     \ |  \1 + tan (4*x)/ *acos(tan(4*x))   6*\1 + tan (4*x)/*tan(4*x)   4*tan (4*x)*acos(tan(4*x))   2*\1 + tan (4*x)/*acos(tan(4*x))   3*\1 + tan (4*x)/ *tan(4*x)   6*\1 + tan (4*x)/ *acos(tan(4*x))*log(3)   6*tan (4*x)*\1 + tan (4*x)/*acos(tan(4*x))   4*\1 + tan (4*x)/ *acos (tan(4*x))*log (3)   3*\1 + tan (4*x)/ *tan (4*x)*acos(tan(4*x))   12*acos (tan(4*x))*\1 + tan (4*x)/*log(3)*tan(4*x)   6*\1 + tan (4*x)/ *acos (tan(4*x))*log(3)*tan(4*x)|       
128*3               *\1 + tan (4*x)/*|- ------------------------------- - -------------------------- - -------------------------- - -------------------------------- + --------------------------- - ---------------------------------------- - ------------------------------------------ - ------------------------------------------ - ------------------------------------------- - -------------------------------------------------- + --------------------------------------------------|*log(3)
                                     |                        3/2                       2                     _______________                 _______________                               2                                  3/2                                         3/2                                          3/2                                           5/2                                         2                                                          2                 |       
                                     |         /       2     \                  -1 + tan (4*x)               /        2                      /        2                     /        2     \                    /       2     \                             /       2     \                              /       2     \                               /       2     \                                    -1 + tan (4*x)                                     /        2     \                  |       
                                     \         \1 - tan (4*x)/                                             \/  1 - tan (4*x)               \/  1 - tan (4*x)                \-1 + tan (4*x)/                    \1 - tan (4*x)/                             \1 - tan (4*x)/                              \1 - tan (4*x)/                               \1 - tan (4*x)/                                                                                       \-1 + tan (4*x)/                  /

128 \cdot 3^{\operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}} \left(\tan^{2}{\left(4 x \right)} + 1\right) \left(- \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(3 \right)} \tan{\left(4 x \right)} \operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}}{\tan^{2}{\left(4 x \right)} - 1} - \frac{6 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)}}{\tan^{2}{\left(4 x \right)} - 1} + \frac{6 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \log{\left(3 \right)} \tan{\left(4 x \right)} \operatorname{acos}^{2}{\left(\tan{\left(4 x \right)} \right)}}{\left(\tan^{2}{\left(4 x \right)} - 1\right)^{2}} + \frac{3 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \tan{\left(4 x \right)}}{\left(\tan^{2}{\left(4 x \right)} - 1\right)^{2}} - \frac{2 \left(\tan^{2}{\left(4 x \right)} + 1\right) \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\sqrt{1 - \tan^{2}{\left(4 x \right)}}} - \frac{4 \tan^{2}{\left(4 x \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\sqrt{1 - \tan^{2}{\left(4 x \right)}}} - \frac{4 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \log{\left(3 \right)}^{2} \operatorname{acos}^{3}{\left(\tan{\left(4 x \right)} \right)}}{\left(1 - \tan^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} - \frac{6 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \log{\left(3 \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\left(1 - \tan^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} - \frac{\left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\left(1 - \tan^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} - \frac{6 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan^{2}{\left(4 x \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\left(1 - \tan^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} - \frac{3 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \tan^{2}{\left(4 x \right)} \operatorname{acos}{\left(\tan{\left(4 x \right)} \right)}}{\left(1 - \tan^{2}{\left(4 x \right)}\right)^{\frac{5}{2}}}\right) \log{\left(3 \right)}

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Gráfico

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Derivada de y=3^arccos^2(tg4x)

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