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y=arccos^4x*ln(x^2+x-1)
Derivada de la función/ x^2+x/ cos^4x/ arccos/ y=arccos^4x*ln(x^2+x-1)

Derivada de y=arccos^4x*ln(x^2+x-1)

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Solución

Ha introducido [src] 
    4       / 2        \
acos (x)*log\x  + x - 1/
log⁡((x2+x)−1)acos⁡4(x)\log{\left(\left(x^{2} + x\right) - 1 \right)} \operatorname{acos}^{4}{\left(x \right)} 
acos(x)^4*log(x^2 + x - 1)
Gráfica
02468-8-6-4-2-1010-500500
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Primera derivada [src] 
    4                      3       / 2        \
acos (x)*(1 + 2*x)   4*acos (x)*log\x  + x - 1/
------------------ - --------------------------
     2                         ________        
    x  + x - 1                /      2         
                            \/  1 - x
(2x+1)acos⁡4(x)(x2+x)−1−4log⁡((x2+x)−1)acos⁡3(x)1−x2\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{\left(x^{2} + x\right) - 1} - \frac{4 \log{\left(\left(x^{2} + x\right) - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
          /                                                      /               2\                            \
          |                                                 2    |      (1 + 2*x) |                            |
          |                                             acos (x)*|-2 + -----------|                            |
          |                                                      |               2|                            |
     2    |  /   3       x*acos(x) \    /          2\            \     -1 + x + x /      8*(1 + 2*x)*acos(x)   |
-acos (x)*|4*|------- + -----------|*log\-1 + x + x / + --------------------------- + -------------------------|
          |  |      2           3/2|                                      2              ________              |
          |  |-1 + x    /     2\   |                            -1 + x + x              /      2  /          2\|
          \  \          \1 - x /   /                                                  \/  1 - x  *\-1 + x + x //
−(((2x+1)2x2+x−1−2)acos⁡2(x)x2+x−1+4(xacos⁡(x)(1−x2)32+3x2−1)log⁡(x2+x−1)+8(2x+1)acos⁡(x)1−x2(x2+x−1))acos⁡2(x)- \left(\frac{\left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 1} - 2\right) \operatorname{acos}^{2}{\left(x \right)}}{x^{2} + x - 1} + 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^{2} + x - 1 \right)} + \frac{8 \left(2 x + 1\right) \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x^{2} + x - 1\right)}\right) \operatorname{acos}^{2}{\left(x \right)}
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Tercera derivada [src] 
  /                                                                                                    /               2\               /   3       x*acos(x) \                      /               2\\        
  |                                                                                     3              |      (1 + 2*x) |   6*(1 + 2*x)*|------- + -----------|*acos(x)         2    |      (1 + 2*x) ||        
  |                                                                                 acos (x)*(1 + 2*x)*|-3 + -----------|               |      2           3/2|           6*acos (x)*|-2 + -----------||        
  |    /                    2                        2     2   \                                       |               2|               |-1 + x    /     2\   |                      |               2||        
  |    |     6          acos (x)    9*x*acos(x)   3*x *acos (x)|    /          2\                      \     -1 + x + x /               \          \1 - x /   /                      \     -1 + x + x /|        
2*|- 2*|----------- + ----------- - ----------- + -------------|*log\-1 + x + x / + ------------------------------------- - ------------------------------------------- + -----------------------------|*acos(x)
  |    |        3/2           3/2             2            5/2 |                                             2                                        2                        ________                |        
  |    |/     2\      /     2\       /      2\     /     2\    |                                /          2\                               -1 + x + x                        /      2  /          2\  |        
  \    \\1 - x /      \1 - x /       \-1 + x /     \1 - x /    /                                \-1 + x + x /                                                               \/  1 - x  *\-1 + x + x /  /
2((2x+1)((2x+1)2x2+x−1−3)acos⁡3(x)(x2+x−1)2−6(2x+1)(xacos⁡(x)(1−x2)32+3x2−1)acos⁡(x)x2+x−1−2(3x2acos⁡2(x)(1−x2)52−9xacos⁡(x)(x2−1)2+acos⁡2(x)(1−x2)32+6(1−x2)32)log⁡(x2+x−1)+6((2x+1)2x2+x−1−2)acos⁡2(x)1−x2(x2+x−1))acos⁡(x)2 \left(\frac{\left(2 x + 1\right) \left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 1} - 3\right) \operatorname{acos}^{3}{\left(x \right)}}{\left(x^{2} + x - 1\right)^{2}} - \frac{6 \left(2 x + 1\right) \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^{2} + x - 1} - 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^{2} + x - 1 \right)} + \frac{6 \left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 1} - 2\right) \operatorname{acos}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x^{2} + x - 1\right)}\right) \operatorname{acos}{\left(x \right)}
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Gráfico
Derivada de y=arccos^4x*ln(x^2+x-1)
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