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y=tg^5(x+2)×arccos3x^2
Derivada de la función/ (x+2)/ cos3x/ arccos/ y=tg^5/ y=tg^5(x+2)×arccos3x^2

Derivada de y=tg^5(x+2)×arccos3x^2

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   5            2     
tan (x + 2)*acos (3*x)
tan⁡5(x+2)acos⁡2(3x)\tan^{5}{\left(x + 2 \right)} \operatorname{acos}^{2}{\left(3 x \right)} 
tan(x + 2)^5*acos(3*x)^2
Gráfica
02468-8-6-4-2-1010-25000000000000002500000000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                                  5                 
    2         4        /         2       \   6*tan (x + 2)*acos(3*x)
acos (3*x)*tan (x + 2)*\5 + 5*tan (x + 2)/ - -----------------------
                                                     __________     
                                                    /        2      
                                                  \/  1 - 9*x
(5tan⁡2(x+2)+5)tan⁡4(x+2)acos⁡2(3x)−6tan⁡5(x+2)acos⁡(3x)1−9x2\left(5 \tan^{2}{\left(x + 2 \right)} + 5\right) \tan^{4}{\left(x + 2 \right)} \operatorname{acos}^{2}{\left(3 x \right)} - \frac{6 \tan^{5}{\left(x + 2 \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}
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Segunda derivada [src] 
              /                                                                                                      /       2       \                     \
     3        |       2        /    1       3*x*acos(3*x)\         2      /       2       \ /         2       \   30*\1 + tan (2 + x)/*acos(3*x)*tan(2 + x)|
2*tan (2 + x)*|- 9*tan (2 + x)*|--------- + -------------| + 5*acos (3*x)*\1 + tan (2 + x)/*\2 + 3*tan (2 + x)/ - -----------------------------------------|
              |                |        2             3/2|                                                                         __________              |
              |                |-1 + 9*x    /       2\   |                                                                        /        2               |
              \                \            \1 - 9*x /   /                                                                      \/  1 - 9*x                /
2(−9(3xacos⁡(3x)(1−9x2)32+19x2−1)tan⁡2(x+2)+5(tan⁡2(x+2)+1)(3tan⁡2(x+2)+2)acos⁡2(3x)−30(tan⁡2(x+2)+1)tan⁡(x+2)acos⁡(3x)1−9x2)tan⁡3(x+2)2 \left(- 9 \left(\frac{3 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \tan^{2}{\left(x + 2 \right)} + 5 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \left(3 \tan^{2}{\left(x + 2 \right)} + 2\right) \operatorname{acos}^{2}{\left(3 x \right)} - \frac{30 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \tan{\left(x + 2 \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\right) \tan^{3}{\left(x + 2 \right)}
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Tercera derivada [src] 
              /                 /                                   2          \                                                                                                  /                                   2                                   \      /       2       \ /         2       \                     \
     2        |        3        |  acos(3*x)         9*x        27*x *acos(3*x)|          2        /       2       \ /    1       3*x*acos(3*x)\         2      /       2       \ |     4            /       2       \          2        /       2       \|   90*\1 + tan (2 + x)/*\2 + 3*tan (2 + x)/*acos(3*x)*tan(2 + x)|
2*tan (2 + x)*|- 27*tan (2 + x)*|------------- - ------------ + ---------------| - 135*tan (2 + x)*\1 + tan (2 + x)/*|--------- + -------------| + 5*acos (3*x)*\1 + tan (2 + x)/*\2*tan (2 + x) + 6*\1 + tan (2 + x)/  + 13*tan (2 + x)*\1 + tan (2 + x)// - -------------------------------------------------------------|
              |                 |          3/2              2              5/2 |                                     |        2             3/2|                                                                                                                                         __________                        |
              |                 |/       2\      /        2\     /       2\    |                                     |-1 + 9*x    /       2\   |                                                                                                                                        /        2                         |
              \                 \\1 - 9*x /      \-1 + 9*x /     \1 - 9*x /    /                                     \            \1 - 9*x /   /                                                                                                                                      \/  1 - 9*x                          /
2(−135(3xacos⁡(3x)(1−9x2)32+19x2−1)(tan⁡2(x+2)+1)tan⁡2(x+2)+5(tan⁡2(x+2)+1)(6(tan⁡2(x+2)+1)2+13(tan⁡2(x+2)+1)tan⁡2(x+2)+2tan⁡4(x+2))acos⁡2(3x)−27(27x2acos⁡(3x)(1−9x2)52−9x(9x2−1)2+acos⁡(3x)(1−9x2)32)tan⁡3(x+2)−90(tan⁡2(x+2)+1)(3tan⁡2(x+2)+2)tan⁡(x+2)acos⁡(3x)1−9x2)tan⁡2(x+2)2 \left(- 135 \left(\frac{3 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \tan^{2}{\left(x + 2 \right)} + 5 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \left(6 \left(\tan^{2}{\left(x + 2 \right)} + 1\right)^{2} + 13 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \tan^{2}{\left(x + 2 \right)} + 2 \tan^{4}{\left(x + 2 \right)}\right) \operatorname{acos}^{2}{\left(3 x \right)} - 27 \left(\frac{27 x^{2} \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{9 x}{\left(9 x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \tan^{3}{\left(x + 2 \right)} - \frac{90 \left(\tan^{2}{\left(x + 2 \right)} + 1\right) \left(3 \tan^{2}{\left(x + 2 \right)} + 2\right) \tan{\left(x + 2 \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\right) \tan^{2}{\left(x + 2 \right)}
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Gráfico
Derivada de y=tg^5(x+2)×arccos3x^2
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