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x*exp(tg(2x)^3*arcsin(4x)-((3x-2)^4)/sin(x)^5-x)
x*exp(tg(2x)^3*arcsin(4x)+((3x-2)^4)/sinx^5-x)
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Derivada de la función/ x*exp(tg(2x)^3*arcsin(4x)+((3x-2)^4)/sin(x)^5-x)

Derivada de xexp(tg(2x)^3arcsin(4x)+((3x-2)^4)/sin(x)^5-x)

Solución

Ha introducido [src]

                                  4    
      3                  (3*x - 2)     
   tan (2*x)*asin(4*x) + ---------- - x
                             5         
                          sin (x)      
x*e

x e^{- x + \left(\frac{\left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)}\right)}

x*exp(tan(2*x)^3*asin(4*x) + (3*x - 2)^4/sin(x)^5 - x)

Primera derivada [src]

                                                                                                                                      4                                       4    
                                                                                                          3                  (3*x - 2)            3                  (3*x - 2)     
                                                                                                       tan (2*x)*asin(4*x) + ---------- - x    tan (2*x)*asin(4*x) + ---------- - x
  /           3                      3                                                      4       \                            5                                       5         
  |      4*tan (2*x)     12*(3*x - 2)       2      /         2     \             5*(3*x - 2) *cos(x)|                         sin (x)                                 sin (x)      
x*|-1 + -------------- + ------------- + tan (2*x)*\6 + 6*tan (2*x)/*asin(4*x) - -------------------|*e                                     + e                                    
  |        ___________         5                                                          6         |                                                                              
  |       /         2       sin (x)                                                    sin (x)      |                                                                              
  \     \/  1 - 16*x                                                                                /

x \left(- \frac{5 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{12 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + \left(6 \tan^{2}{\left(2 x \right)} + 6\right) \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} - 1 + \frac{4 \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right) e^{- x + \left(\frac{\left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)}\right)} + e^{- x + \left(\frac{\left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)}\right)}

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Segunda derivada [src]

                                                                                                                                                                                                                                                                                                                                                                                                                                                           4                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                 (-2 + 3*x)       3               
/       /                                                                                                     2                                                                                                                                                                                                                      \                                                                                                   \  -x + ----------- + tan (2*x)*asin(4*x)
|       |/           3                       3               4                                               \                4                 2                 3                            2                                                                            4    2            2      /       2     \           3     |         3                       3                4                                                |            5                           
|       ||      4*tan (2*x)     12*(-2 + 3*x)    5*(-2 + 3*x) *cos(x)        2      /       2     \          |    5*(-2 + 3*x)    108*(-2 + 3*x)    120*(-2 + 3*x) *cos(x)      /       2     \                             3      /       2     \             30*(-2 + 3*x) *cos (x)   48*tan (2*x)*\1 + tan (2*x)/   64*x*tan (2*x)|    8*tan (2*x)     24*(-2 + 3*x)    10*(-2 + 3*x) *cos(x)         2      /       2     \          |         sin (x)                        
|-2 + x*||-1 + -------------- + -------------- - -------------------- + 6*tan (2*x)*\1 + tan (2*x)/*asin(4*x)|  + ------------- + --------------- - ---------------------- + 24*\1 + tan (2*x)/ *asin(4*x)*tan(2*x) + 24*tan (2*x)*\1 + tan (2*x)/*asin(4*x) + ---------------------- + ---------------------------- + --------------| + -------------- + -------------- - --------------------- + 12*tan (2*x)*\1 + tan (2*x)/*asin(4*x)|*e                                      
|       ||        ___________         5                   6                                                  |          5                5                    6                                                                                                          7                        ___________                     3/2|      ___________         5                    6                                                   |                                        
|       ||       /         2       sin (x)             sin (x)                                               |       sin (x)          sin (x)              sin (x)                                                                                                    sin (x)                    /         2           /        2\   |     /         2       sin (x)              sin (x)                                                |                                        
\       \\     \/  1 - 16*x                                                                                  /                                                                                                                                                                                 \/  1 - 16*x            \1 - 16*x /   /   \/  1 - 16*x                                                                                    /

\left(x \left(\frac{64 x \tan^{3}{\left(2 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{5 \left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \frac{30 \left(3 x - 2\right)^{4} \cos^{2}{\left(x \right)}}{\sin^{7}{\left(x \right)}} - \frac{120 \left(3 x - 2\right)^{3} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{108 \left(3 x - 2\right)^{2}}{\sin^{5}{\left(x \right)}} + 24 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + 24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + \left(- \frac{5 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{12 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + 6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} - 1 + \frac{4 \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right)^{2} + \frac{48 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right) - \frac{10 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{24 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + 12 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} - 2 + \frac{8 \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right) e^{- x + \frac{\left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)}}

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Tercera derivada [src]

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       4                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             (-2 + 3*x)       3               
/                                                                                                       2     /                                                                                                     3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               2                                                                                                                                                                      \                                                                                                                                                                                                                         \  -x + ----------- + tan (2*x)*asin(4*x)
|  /           3                       3               4                                               \      |/           3                       3               4                                               \      /           3                       3               4                                               \ /            4                 2                 3                            2                                                                            4    2            2      /       2     \           3     \                     3                    3                       3                                   2                        4    3                   4                                                       /       2     \                    3      /       2     \                      2                                      3    2            2    3                  2      /       2     \|                4                 2                 3                            2                                                                            4    2             2      /       2     \            3     |            5                           
|  |      4*tan (2*x)     12*(-2 + 3*x)    5*(-2 + 3*x) *cos(x)        2      /       2     \          |      ||      4*tan (2*x)     12*(-2 + 3*x)    5*(-2 + 3*x) *cos(x)        2      /       2     \          |      |      4*tan (2*x)     12*(-2 + 3*x)    5*(-2 + 3*x) *cos(x)        2      /       2     \          | |5*(-2 + 3*x)    108*(-2 + 3*x)    120*(-2 + 3*x) *cos(x)      /       2     \                             3      /       2     \             30*(-2 + 3*x) *cos (x)   48*tan (2*x)*\1 + tan (2*x)/   64*x*tan (2*x)|      /       2     \               64*tan (2*x)    180*(-2 + 3*x)    648*(-2 + 3*x)   1620*(-2 + 3*x) *cos(x)   210*(-2 + 3*x) *cos (x)   85*(-2 + 3*x) *cos(x)         4      /       2     \             288*\1 + tan (2*x)/ *tan(2*x)   288*tan (2*x)*\1 + tan (2*x)/       /       2     \     2                  1080*(-2 + 3*x) *cos (x)   3072*x *tan (2*x)   1152*x*tan (2*x)*\1 + tan (2*x)/|   15*(-2 + 3*x)    324*(-2 + 3*x)    360*(-2 + 3*x) *cos(x)      /       2     \                             3      /       2     \             90*(-2 + 3*x) *cos (x)   144*tan (2*x)*\1 + tan (2*x)/   192*x*tan (2*x)|         sin (x)                        
|3*|-1 + -------------- + -------------- - -------------------- + 6*tan (2*x)*\1 + tan (2*x)/*asin(4*x)|  + x*||-1 + -------------- + -------------- - -------------------- + 6*tan (2*x)*\1 + tan (2*x)/*asin(4*x)|  + 3*|-1 + -------------- + -------------- - -------------------- + 6*tan (2*x)*\1 + tan (2*x)/*asin(4*x)|*|------------- + --------------- - ---------------------- + 24*\1 + tan (2*x)/ *asin(4*x)*tan(2*x) + 24*tan (2*x)*\1 + tan (2*x)/*asin(4*x) + ---------------------- + ---------------------------- + --------------| + 48*\1 + tan (2*x)/ *asin(4*x) + -------------- + --------------- + -------------- - ----------------------- - ----------------------- - --------------------- + 96*tan (2*x)*\1 + tan (2*x)/*asin(4*x) + ----------------------------- + ----------------------------- + 336*\1 + tan (2*x)/ *tan (2*x)*asin(4*x) + ------------------------ + ----------------- + --------------------------------| + -------------- + --------------- - ---------------------- + 72*\1 + tan (2*x)/ *asin(4*x)*tan(2*x) + 72*tan (2*x)*\1 + tan (2*x)/*asin(4*x) + ---------------------- + ----------------------------- + ---------------|*e                                      
|  |        ___________         5                   6                                                  |      ||        ___________         5                   6                                                  |      |        ___________         5                   6                                                  | |      5                5                    6                                                                                                          7                        ___________                     3/2|                                              3/2          5                5                     6                         8                        6                                                                 ___________                     ___________                                                                7                            5/2                        3/2         |         5                 5                    6                                                                                                          7                         ___________                      3/2|                                        
|  |       /         2       sin (x)             sin (x)                                               |      ||       /         2       sin (x)             sin (x)                                               |      |       /         2       sin (x)             sin (x)                                               | |   sin (x)          sin (x)              sin (x)                                                                                                    sin (x)                    /         2           /        2\   |                                   /        2\          sin (x)          sin (x)               sin (x)                   sin (x)                  sin (x)                                                             /         2                     /         2                                                              sin (x)              /        2\                /        2\            |      sin (x)           sin (x)              sin (x)                                                                                                    sin (x)                     /         2            /        2\   |                                        
\  \     \/  1 - 16*x                                                                                  /      \\     \/  1 - 16*x                                                                                  /      \     \/  1 - 16*x                                                                                  / \                                                                                                                                                                             \/  1 - 16*x            \1 - 16*x /   /                                   \1 - 16*x /                                                                                                                                                                      \/  1 - 16*x                    \/  1 - 16*x                                                                                    \1 - 16*x /                \1 - 16*x /            /                                                                                                                                                                                  \/  1 - 16*x             \1 - 16*x /   /

\left(x \left(\frac{3072 x^{2} \tan^{3}{\left(2 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} + \frac{1152 x \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{85 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} - \frac{210 \left(3 x - 2\right)^{4} \cos^{3}{\left(x \right)}}{\sin^{8}{\left(x \right)}} + \frac{180 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + \frac{1080 \left(3 x - 2\right)^{3} \cos^{2}{\left(x \right)}}{\sin^{7}{\left(x \right)}} - \frac{1620 \left(3 x - 2\right)^{2} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{648 \left(3 x - 2\right)}{\sin^{5}{\left(x \right)}} + 48 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \operatorname{asin}{\left(4 x \right)} + 336 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + 96 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{4}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + \left(- \frac{5 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{12 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + 6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} - 1 + \frac{4 \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right)^{3} + 3 \left(- \frac{5 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{12 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + 6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} - 1 + \frac{4 \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right) \left(\frac{64 x \tan^{3}{\left(2 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{5 \left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \frac{30 \left(3 x - 2\right)^{4} \cos^{2}{\left(x \right)}}{\sin^{7}{\left(x \right)}} - \frac{120 \left(3 x - 2\right)^{3} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{108 \left(3 x - 2\right)^{2}}{\sin^{5}{\left(x \right)}} + 24 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + 24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + \frac{48 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right) + \frac{288 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}} + \frac{288 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}} + \frac{64 \tan^{3}{\left(2 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right) + \frac{192 x \tan^{3}{\left(2 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{15 \left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \frac{90 \left(3 x - 2\right)^{4} \cos^{2}{\left(x \right)}}{\sin^{7}{\left(x \right)}} - \frac{360 \left(3 x - 2\right)^{3} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{324 \left(3 x - 2\right)^{2}}{\sin^{5}{\left(x \right)}} + 72 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + 72 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} + 3 \left(- \frac{5 \left(3 x - 2\right)^{4} \cos{\left(x \right)}}{\sin^{6}{\left(x \right)}} + \frac{12 \left(3 x - 2\right)^{3}}{\sin^{5}{\left(x \right)}} + 6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)} - 1 + \frac{4 \tan^{3}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right)^{2} + \frac{144 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan^{2}{\left(2 x \right)}}{\sqrt{1 - 16 x^{2}}}\right) e^{- x + \frac{\left(3 x - 2\right)^{4}}{\sin^{5}{\left(x \right)}} + \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(4 x \right)}}

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Expresiones semejantes

Expresiones con funciones

Derivada de xexp(tg(2x)^3arcsin(4x)+((3x-2)^4)/sin(x)^5-x)

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Derivada de x*exp(tg(2x)^3*arcsin(4x)+((3x-2)^4)/sin(x)^5-x)

Gráfico:

Definida a trozos:

Solución

Derivada de xexp(tg(2x)^3arcsin(4x)+((3x-2)^4)/sin(x)^5-x)