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y=arccos^4xln(x-3)
Derivada de la función/ (x-3)/ cos^4x/ arccos/ y=arccos^4xln(x-3)

Derivada de y=arccos^4xln(x-3)

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

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Solución

Ha introducido [src] 
    4              
acos (x)*log(x - 3)
log⁡(x−3)acos⁡4(x)\log{\left(x - 3 \right)} \operatorname{acos}^{4}{\left(x \right)} 
acos(x)^4*log(x - 3)
Gráfica
02468-8-6-4-2-1010-200200
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Trazar el gráfico f'(x)
Primera derivada [src] 
    4            3              
acos (x)   4*acos (x)*log(x - 3)
-------- - ---------------------
 x - 3             ________     
                  /      2      
                \/  1 - x
acos⁡4(x)x−3−4log⁡(x−3)acos⁡3(x)1−x2\frac{\operatorname{acos}^{4}{\left(x \right)}}{x - 3} - \frac{4 \log{\left(x - 3 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
          /     2                                                                  \
     2    | acos (x)     /   3       x*acos(x) \                    8*acos(x)      |
-acos (x)*|--------- + 4*|------- + -----------|*log(-3 + x) + --------------------|
          |        2     |      2           3/2|                  ________         |
          |(-3 + x)      |-1 + x    /     2\   |                 /      2          |
          \              \          \1 - x /   /               \/  1 - x  *(-3 + x)/
−(4(xacos⁡(x)(1−x2)32+3x2−1)log⁡(x−3)+acos⁡2(x)(x−3)2+8acos⁡(x)1−x2(x−3))acos⁡2(x)- \left(4 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{x^{2} - 1}\right) \log{\left(x - 3 \right)} + \frac{\operatorname{acos}^{2}{\left(x \right)}}{\left(x - 3\right)^{2}} + \frac{8 \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x - 3\right)}\right) \operatorname{acos}^{2}{\left(x \right)}
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Tercera derivada [src] 
  /                                                                                        /   3       x*acos(x) \                                \        
  |                                                                                      6*|------- + -----------|*acos(x)                        |        
  |                                                                                        |      2           3/2|                                |        
  |     3        /                    2                        2     2   \                 |-1 + x    /     2\   |                       2        |        
  | acos (x)     |     6          acos (x)    9*x*acos(x)   3*x *acos (x)|                 \          \1 - x /   /                 6*acos (x)     |        
2*|--------- - 2*|----------- + ----------- - ----------- + -------------|*log(-3 + x) - --------------------------------- + ---------------------|*acos(x)
  |        3     |        3/2           3/2             2            5/2 |                             -3 + x                   ________          |        
  |(-3 + x)      |/     2\      /     2\       /      2\     /     2\    |                                                     /      2          2|        
  \              \\1 - x /      \1 - x /       \-1 + x /     \1 - x /    /                                                   \/  1 - x  *(-3 + x) /
2(−2(3x2acos⁡2(x)(1−x2)52−9xacos⁡(x)(x2−1)2+acos⁡2(x)(1−x2)32+6(1−x2)32)log⁡(x−3)−6(xacos⁡(x)(1−x2)32+3x2−1)acos⁡(x)x−3+acos⁡3(x)(x−3)3+6acos⁡2(x)1−x2(x−3)2)acos⁡(x)2 \left(- 2 \left(\frac{3 x^{2} \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{9 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{6}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(x - 3 \right)} - \frac{6 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{x^{2} - 1}\right) \operatorname{acos}{\left(x \right)}}{x - 3} + \frac{\operatorname{acos}^{3}{\left(x \right)}}{\left(x - 3\right)^{3}} + \frac{6 \operatorname{acos}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x - 3\right)^{2}}\right) \operatorname{acos}{\left(x \right)}
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Gráfico
Derivada de y=arccos^4xln(x-3)
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