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y=(1/3)^arccosx²
Derivada de la función/ cosx²/ arccos/ y=(1/3)^arccosx²

Derivada de y=(1/3)^arccosx²

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Solución

Ha introducido [src] 
      2   
 -acos (x)
3
(13)acos⁡2(x)\left(\frac{1}{3}\right)^{\operatorname{acos}^{2}{\left(x \right)}} 
(1/3)^(acos(x)^2)
Gráfica
02468-8-6-4-2-1010-5000050000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        2                  
   -acos (x)               
2*3         *acos(x)*log(3)
---------------------------
           ________        
          /      2         
        \/  1 - x
2⋅3−acos⁡2(x)log⁡(3)acos⁡(x)1−x2\frac{2 \cdot 3^{- \operatorname{acos}^{2}{\left(x \right)}} \log{\left(3 \right)} \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
        2    /                              2          \       
   -acos (x) |   1       x*acos(x)    2*acos (x)*log(3)|       
2*3         *|------- + ----------- - -----------------|*log(3)
             |      2           3/2              2     |       
             |-1 + x    /     2\           -1 + x      |       
             \          \1 - x /                       /
2⋅3−acos⁡2(x)(xacos⁡(x)(1−x2)32−2log⁡(3)acos⁡2(x)x2−1+1x2−1)log⁡(3)2 \cdot 3^{- \operatorname{acos}^{2}{\left(x \right)}} \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \log{\left(3 \right)} \operatorname{acos}^{2}{\left(x \right)}}{x^{2} - 1} + \frac{1}{x^{2} - 1}\right) \log{\left(3 \right)}
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Tercera derivada [src] 
        2    /                                                 2                 3       2              2          \       
   -acos (x) |  acos(x)        3*x       6*acos(x)*log(3)   3*x *acos(x)   4*acos (x)*log (3)   6*x*acos (x)*log(3)|       
2*3         *|----------- - ---------- - ---------------- + ------------ + ------------------ + -------------------|*log(3)
             |        3/2            2             3/2              5/2               3/2                     2    |       
             |/     2\      /      2\      /     2\         /     2\          /     2\               /      2\     |       
             \\1 - x /      \-1 + x /      \1 - x /         \1 - x /          \1 - x /               \-1 + x /     /
2⋅3−acos⁡2(x)(3x2acos⁡(x)(1−x2)52+6xlog⁡(3)acos⁡2(x)(x2−1)2−3x(x2−1)2+4log⁡(3)2acos⁡3(x)(1−x2)32−6log⁡(3)acos⁡(x)(1−x2)32+acos⁡(x)(1−x2)32)log⁡(3)2 \cdot 3^{- \operatorname{acos}^{2}{\left(x \right)}} \left(\frac{3 x^{2} \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \log{\left(3 \right)} \operatorname{acos}^{2}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{4 \log{\left(3 \right)}^{2} \operatorname{acos}^{3}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 \log{\left(3 \right)} \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(3 \right)}
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Gráfico
Derivada de y=(1/3)^arccosx²
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