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y=tg^4(3x)*arcsin2x^2
Derivada de la función/ sin2x/ y=tg^4/ arcsin/ y=tg^4(3x)*arcsin2x^2

Derivada de y=tg^4(3x)*arcsin2x^2

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   4          2     
tan (3*x)*asin (2*x)
tan⁡4(3x)asin⁡2(2x)\tan^{4}{\left(3 x \right)} \operatorname{asin}^{2}{\left(2 x \right)} 
tan(3*x)^4*asin(2*x)^2
Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
                                                4               
    2         3      /           2     \   4*tan (3*x)*asin(2*x)
asin (2*x)*tan (3*x)*\12 + 12*tan (3*x)/ + ---------------------
                                                  __________    
                                                 /        2     
                                               \/  1 - 4*x
(12tan⁡2(3x)+12)tan⁡3(3x)asin⁡2(2x)+4tan⁡4(3x)asin⁡(2x)1−4x2\left(12 \tan^{2}{\left(3 x \right)} + 12\right) \tan^{3}{\left(3 x \right)} \operatorname{asin}^{2}{\left(2 x \right)} + \frac{4 \tan^{4}{\left(3 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}
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Segunda derivada [src] 
            /                                                                                                /       2     \                   \
     2      |     2      /      1       2*x*asin(2*x)\         2      /       2     \ /         2     \   24*\1 + tan (3*x)/*asin(2*x)*tan(3*x)|
4*tan (3*x)*|2*tan (3*x)*|- --------- + -------------| + 9*asin (2*x)*\1 + tan (3*x)/*\3 + 5*tan (3*x)/ + -------------------------------------|
            |            |          2             3/2|                                                                   __________            |
            |            |  -1 + 4*x    /       2\   |                                                                  /        2             |
            \            \              \1 - 4*x /   /                                                                \/  1 - 4*x              /
4(2(2xasin⁡(2x)(1−4x2)32−14x2−1)tan⁡2(3x)+9(tan⁡2(3x)+1)(5tan⁡2(3x)+3)asin⁡2(2x)+24(tan⁡2(3x)+1)tan⁡(3x)asin⁡(2x)1−4x2)tan⁡2(3x)4 \left(2 \left(\frac{2 x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \tan^{2}{\left(3 x \right)} + 9 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(5 \tan^{2}{\left(3 x \right)} + 3\right) \operatorname{asin}^{2}{\left(2 x \right)} + \frac{24 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \tan^{2}{\left(3 x \right)}
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Tercera derivada [src] 
  /            /                                   2          \                                 /                               2                               \                                                                   /       2     \ /         2     \                   \         
  |     3      |  asin(2*x)         6*x        12*x *asin(2*x)|          2      /       2     \ |     4          /       2     \          2      /       2     \|         2      /       2     \ /      1       2*x*asin(2*x)\   54*\1 + tan (3*x)/*\3 + 5*tan (3*x)/*asin(2*x)*tan(3*x)|         
8*|2*tan (3*x)*|------------- + ------------ + ---------------| + 27*asin (2*x)*\1 + tan (3*x)/*\2*tan (3*x) + 3*\1 + tan (3*x)/  + 10*tan (3*x)*\1 + tan (3*x)// + 36*tan (3*x)*\1 + tan (3*x)/*|- --------- + -------------| + -------------------------------------------------------|*tan(3*x)
  |            |          3/2              2              5/2 |                                                                                                                                  |          2             3/2|                           __________                     |         
  |            |/       2\      /        2\     /       2\    |                                                                                                                                  |  -1 + 4*x    /       2\   |                          /        2                      |         
  \            \\1 - 4*x /      \-1 + 4*x /     \1 - 4*x /    /                                                                                                                                  \              \1 - 4*x /   /                        \/  1 - 4*x                       /
8(36(2xasin⁡(2x)(1−4x2)32−14x2−1)(tan⁡2(3x)+1)tan⁡2(3x)+27(tan⁡2(3x)+1)(3(tan⁡2(3x)+1)2+10(tan⁡2(3x)+1)tan⁡2(3x)+2tan⁡4(3x))asin⁡2(2x)+2(12x2asin⁡(2x)(1−4x2)52+6x(4x2−1)2+asin⁡(2x)(1−4x2)32)tan⁡3(3x)+54(tan⁡2(3x)+1)(5tan⁡2(3x)+3)tan⁡(3x)asin⁡(2x)1−4x2)tan⁡(3x)8 \left(36 \left(\frac{2 x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan^{2}{\left(3 x \right)} + 27 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(3 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} + 10 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan^{2}{\left(3 x \right)} + 2 \tan^{4}{\left(3 x \right)}\right) \operatorname{asin}^{2}{\left(2 x \right)} + 2 \left(\frac{12 x^{2} \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{6 x}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right) \tan^{3}{\left(3 x \right)} + \frac{54 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(5 \tan^{2}{\left(3 x \right)} + 3\right) \tan{\left(3 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \tan{\left(3 x \right)}
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Gráfico
Derivada de y=tg^4(3x)*arcsin2x^2
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