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y=arccos^3x*ln^2(3x)
Derivada de la función/ arccos/ cos^3/ x*ln^2/ y=arccos^3x*ln^2(3x)

Derivada de y=arccos^3x*ln^2(3x)

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

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Solución

Ha introducido [src] 
    3       2     
acos (x)*log (3*x)
log⁡(3x)2acos⁡3(x)\log{\left(3 x \right)}^{2} \operatorname{acos}^{3}{\left(x \right)} 
acos(x)^3*log(3*x)^2
Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
        2       2              3            
  3*acos (x)*log (3*x)   2*acos (x)*log(3*x)
- -------------------- + -------------------
         ________                 x         
        /      2                            
      \/  1 - x
−3log⁡(3x)2acos⁡2(x)1−x2+2log⁡(3x)acos⁡3(x)x- \frac{3 \log{\left(3 x \right)}^{2} \operatorname{acos}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{2 \log{\left(3 x \right)} \operatorname{acos}^{3}{\left(x \right)}}{x}
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Segunda derivada [src] 
 /                                            2                                         \        
 |     2      /   2       x*acos(x) \   2*acos (x)*(-1 + log(3*x))   12*acos(x)*log(3*x)|        
-|3*log (3*x)*|------- + -----------| + -------------------------- + -------------------|*acos(x)
 |            |      2           3/2|                2                       ________   |        
 |            |-1 + x    /     2\   |               x                       /      2    |        
 \            \          \1 - x /   /                                   x*\/  1 - x     /
−(3(xacos⁡(x)(1−x2)32+2x2−1)log⁡(3x)2+12log⁡(3x)acos⁡(x)x1−x2+2(log⁡(3x)−1)acos⁡2(x)x2)acos⁡(x)- \left(3 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} - 1}\right) \log{\left(3 x \right)}^{2} + \frac{12 \log{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{x \sqrt{1 - x^{2}}} + \frac{2 \left(\log{\left(3 x \right)} - 1\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{acos}{\left(x \right)}
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Tercera derivada [src] 
                                                                                                            /   2       x*acos(x) \                                               
                                                                                                         18*|------- + -----------|*acos(x)*log(3*x)                              
                                                                                                            |      2           3/2|                                               
              /                    2                        2     2   \         3                           |-1 + x    /     2\   |                           2                   
       2      |     2          acos (x)    6*x*acos(x)   3*x *acos (x)|   2*acos (x)*(-3 + 2*log(3*x))      \          \1 - x /   /                    18*acos (x)*(-1 + log(3*x))
- 3*log (3*x)*|----------- + ----------- - ----------- + -------------| + ---------------------------- - ------------------------------------------- + ---------------------------
              |        3/2           3/2             2            5/2 |                 3                                     x                                     ________      
              |/     2\      /     2\       /      2\     /     2\    |                x                                                                       2   /      2       
              \\1 - x /      \1 - x /       \-1 + x /     \1 - x /    /                                                                                       x *\/  1 - x
−3(3x2acos⁡2(x)(1−x2)52−6xacos⁡(x)(x2−1)2+acos⁡2(x)(1−x2)32+2(1−x2)32)log⁡(3x)2−18(xacos⁡(x)(1−x2)32+2x2−1)log⁡(3x)acos⁡(x)x+18(log⁡(3x)−1)acos⁡2(x)x21−x2+2(2log⁡(3x)−3)acos⁡3(x)x3- 3 \left(\frac{3 x^{2} \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x \operatorname{acos}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(3 x \right)}^{2} - \frac{18 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} - 1}\right) \log{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{x} + \frac{18 \left(\log{\left(3 x \right)} - 1\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \left(2 \log{\left(3 x \right)} - 3\right) \operatorname{acos}^{3}{\left(x \right)}}{x^{3}}
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Gráfico
Derivada de y=arccos^3x*ln^2(3x)
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