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y=(x+1)arccos(3(x^4))

Derivada de y=(x+1)arccos(3(x^4))

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Solución

Ha introducido [src]
            /   4\
(x + 1)*acos\3*x /
$$\left(x + 1\right) \operatorname{acos}{\left(3 x^{4} \right)}$$
(x + 1)*acos(3*x^4)
Gráfica
Primera derivada [src]
      3                     
  12*x *(x + 1)       /   4\
- ------------- + acos\3*x /
     __________             
    /        8              
  \/  1 - 9*x               
$$- \frac{12 x^{3} \left(x + 1\right)}{\sqrt{1 - 9 x^{8}}} + \operatorname{acos}{\left(3 x^{4} \right)}$$
Segunda derivada [src]
      /                 /           8  \\
    2 |                 |       12*x   ||
12*x *|-2*x + 3*(1 + x)*|-1 + ---------||
      |                 |             8||
      \                 \     -1 + 9*x //
-----------------------------------------
                 __________              
                /        8               
              \/  1 - 9*x                
$$\frac{12 x^{2} \left(- 2 x + 3 \left(x + 1\right) \left(\frac{12 x^{8}}{9 x^{8} - 1} - 1\right)\right)}{\sqrt{1 - 9 x^{8}}}$$
Tercera derivada [src]
     /            /          8            16   \       /           8  \\
     |            |      78*x        648*x     |       |       12*x   ||
36*x*|- 2*(1 + x)*|1 - --------- + ------------| + 3*x*|-1 + ---------||
     |            |            8              2|       |             8||
     |            |    -1 + 9*x    /        8\ |       \     -1 + 9*x /|
     \            \                \-1 + 9*x / /                       /
------------------------------------------------------------------------
                                __________                              
                               /        8                               
                             \/  1 - 9*x                                
$$\frac{36 x \left(3 x \left(\frac{12 x^{8}}{9 x^{8} - 1} - 1\right) - 2 \left(x + 1\right) \left(\frac{648 x^{16}}{\left(9 x^{8} - 1\right)^{2}} - \frac{78 x^{8}}{9 x^{8} - 1} + 1\right)\right)}{\sqrt{1 - 9 x^{8}}}$$
Gráfico
Derivada de y=(x+1)arccos(3(x^4))