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xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))*exp(-x)
Derivada de la función/ xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))*exp(-x)

Derivada de xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))*exp(-x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
     /             2    \    
     |/    ___    \     |    
     |\5*\/ x  + 1/  - 1|  -x
x*tan|------------------|*e  
     |       ___        |    
     \   5*\/ x  + 1    /
xtan⁡((5x+1)2−15x+1)e−xx \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} e^{- x} 
(x*tan(((5*sqrt(x) + 1)^2 - 1)/(5*sqrt(x) + 1)))*exp(-x)
Gráfica
02468-8-6-4-2-1010-200200
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Trazar el gráfico f'(x)
Primera derivada [src] 
/  /        /             2    \\ /          /             2    \\      /             2    \\                /             2    \
|  |        |/    ___    \     || |          |/    ___    \     ||      |/    ___    \     ||                |/    ___    \     |
|  |       2|\5*\/ x  + 1/  - 1|| |  5     5*\\5*\/ x  + 1/  - 1/|      |\5*\/ x  + 1/  - 1||  -x      -x    |\5*\/ x  + 1/  - 1|
|x*|1 + tan |------------------||*|----- - ----------------------| + tan|------------------||*e   - x*e  *tan|------------------|
|  |        |       ___        || |  ___                        2|      |       ___        ||                |       ___        |
|  \        \   5*\/ x  + 1    // |\/ x        ___ /    ___    \ |      \   5*\/ x  + 1    /|                \   5*\/ x  + 1    /
\                                 \        2*\/ x *\5*\/ x  + 1/ /                          /
−xe−xtan⁡((5x+1)2−15x+1)+(x(5x−5((5x+1)2−1)2x(5x+1)2)(tan⁡2((5x+1)2−15x+1)+1)+tan⁡((5x+1)2−15x+1))e−x- x e^{- x} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + \left(x \left(\frac{5}{\sqrt{x}} - \frac{5 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{2 \sqrt{x} \left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right) + \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}\right) e^{- x}
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Segunda derivada [src] 
/                                                                                              /  /                                                                                                        2                         \                              \                                                                    \    
|                                                                                              |  |                                                                               /                      2\     /                  2\|     /                      2\|                                                                    |    
|                                                                                              |  |                                                                               |         /        ___\ |     |     /        ___\ ||     |         /        ___\ ||                                                                    |    
|                                                                                              |  |                                                                               |    -1 + \1 + 5*\/ x / |     |-1 + \1 + 5*\/ x / ||     |    -1 + \1 + 5*\/ x / ||                                                                    |    
|                                                                                              |  |                                                                            10*|2 - -------------------| *tan|-------------------||   4*|2 - -------------------||                                                                    |    
|                                                              /        /                  2\\ |  |                                             2      /                  2\      |                    2  |     |            ___    ||     |                    2  ||                                                                    |    
|                                                              |        |     /        ___\ || |  |                                /        ___\       |     /        ___\ |      |       /        ___\   |     \    1 + 5*\/ x     /|     |       /        ___\   ||                                                                    |    
|                                                              |       2|-1 + \1 + 5*\/ x / || |  |   2            10         -1 + \1 + 5*\/ x /    10*\-1 + \1 + 5*\/ x / /      \       \1 + 5*\/ x /   /                          |     \       \1 + 5*\/ x /   /|                                                                    |    
|                                                            5*|1 + tan |-------------------||*|x*|- ---- - --------------- + ------------------- + ------------------------ + ------------------------------------------------------| + ---------------------------|                                                                    |    
|       /                  2\        /                  2\     |        |            ___    || |  |   3/2     /        ___\                     2                      3                                 x                           |                ___           |           /        /                  2\\ /                      2\|    
|       |     /        ___\ |        |     /        ___\ |     \        \    1 + 5*\/ x     // |  |  x      x*\1 + 5*\/ x /    3/2 /        ___\          /        ___\                                                              |              \/ x            |           |        |     /        ___\ || |         /        ___\ ||    
|       |-1 + \1 + 5*\/ x / |        |-1 + \1 + 5*\/ x / |                                     \  \                           x   *\1 + 5*\/ x /        x*\1 + 5*\/ x /                                                              /                              /       ___ |       2|-1 + \1 + 5*\/ x / || |    -1 + \1 + 5*\/ x / ||  -x
|- 2*tan|-------------------| + x*tan|-------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - 5*\/ x *|1 + tan |-------------------||*|2 - -------------------||*e  
|       |            ___    |        |            ___    |                                                                                                      4                                                                                                               |        |            ___    || |                    2  ||    
|       \    1 + 5*\/ x     /        \    1 + 5*\/ x     /                                                                                                                                                                                                                      \        \    1 + 5*\/ x     // |       /        ___\   ||    
\                                                                                                                                                                                                                                                                                                               \       \1 + 5*\/ x /   //
(−5x(2−(5x+1)2−1(5x+1)2)(tan⁡2((5x+1)2−15x+1)+1)+xtan⁡((5x+1)2−15x+1)+5(x(10(2−(5x+1)2−1(5x+1)2)2tan⁡((5x+1)2−15x+1)x−10x(5x+1)+10((5x+1)2−1)x(5x+1)3−2x32+(5x+1)2−1x32(5x+1)2)+4(2−(5x+1)2−1(5x+1)2)x)(tan⁡2((5x+1)2−15x+1)+1)4−2tan⁡((5x+1)2−15x+1))e−x\left(- 5 \sqrt{x} \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right) + x \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + \frac{5 \left(x \left(\frac{10 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{2} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x} - \frac{10}{x \left(5 \sqrt{x} + 1\right)} + \frac{10 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} - \frac{2}{x^{\frac{3}{2}}} + \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) + \frac{4 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)}{\sqrt{x}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{4} - 2 \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}\right) e^{- x}
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Tercera derivada [src] 
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|                                                                                             |  |                                                                               /                      2\     /                  2\|     /                      2\|                                     |           |                                                                                                                                    /                      2\  /        /                  2\\       /                      2\      /                  2\      /                      2\ /                                           2      /                  2\\    /                  2\|                                                                             /                      2\     /                  2\|                                                                     |    
|                                                                                             |  |                                                                               |         /        ___\ |     |     /        ___\ ||     |         /        ___\ ||                                     |           |                                                                                                                                    |         /        ___\ |  |        |     /        ___\ ||       |         /        ___\ |      |     /        ___\ |      |         /        ___\ | |                              /        ___\       |     /        ___\ ||    |     /        ___\ ||                                                                             |         /        ___\ |     |     /        ___\ ||                                                                     |    
|                                                                                             |  |                                                                               |    -1 + \1 + 5*\/ x / |     |-1 + \1 + 5*\/ x / ||     |    -1 + \1 + 5*\/ x / ||                                     |           |                                                                                                                                    |    -1 + \1 + 5*\/ x / |  |       2|-1 + \1 + 5*\/ x / ||       |    -1 + \1 + 5*\/ x / |     2|-1 + \1 + 5*\/ x / |      |    -1 + \1 + 5*\/ x / | | 2            10         -1 + \1 + 5*\/ x /    10*\-1 + \1 + 5*\/ x / /|    |-1 + \1 + 5*\/ x / ||                                                                             |    -1 + \1 + 5*\/ x / |     |-1 + \1 + 5*\/ x / ||                                                                     |    
|                                                                                             |  |                                                                            10*|2 - -------------------| *tan|-------------------||   4*|2 - -------------------||                                     |           |                                                                                                                                 50*|2 - -------------------| *|1 + tan |-------------------||   100*|2 - -------------------| *tan |-------------------|   30*|2 - -------------------|*|---- + --------------- - ------------------- - ------------------------|*tan|-------------------||                                                                          60*|2 - -------------------| *tan|-------------------||                                                                     |    
|                                                             /        /                  2\\ |  |                                             2      /                  2\      |                    2  |     |            ___    ||     |                    2  ||     /        /                  2\\ |           |                                                    /                  2\      /                  2\     /                  2\      |                    2  |  |        |            ___    ||       |                    2  |      |            ___    |      |                    2  | | 3/2     /        ___\                     2                      3    |    |            ___    ||                       /                  2\      /                  2\      |                    2  |     |            ___    ||            /        /                  2\\ /                      2\|    
|                                                             |        |     /        ___\ || |  |                                /        ___\       |     /        ___\ |      |       /        ___\   |     \    1 + 5*\/ x     /|     |       /        ___\   ||     |        |     /        ___\ || |           |                                                    |     /        ___\ |      |     /        ___\ |     |     /        ___\ |      |       /        ___\   |  \        \    1 + 5*\/ x     //       |       /        ___\   |      \    1 + 5*\/ x     /      |       /        ___\   | |x      x*\1 + 5*\/ x /    3/2 /        ___\          /        ___\     |    \    1 + 5*\/ x     /|                       |     /        ___\ |      |     /        ___\ |      |       /        ___\   |     \    1 + 5*\/ x     /|            |        |     /        ___\ || |         /        ___\ ||    
|                                                             |       2|-1 + \1 + 5*\/ x / || |  |   2            10         -1 + \1 + 5*\/ x /    10*\-1 + \1 + 5*\/ x / /      \       \1 + 5*\/ x /   /                          |     \       \1 + 5*\/ x /   /|     |       2|-1 + \1 + 5*\/ x / || |   12      | 6            30                  150           150*\-1 + \1 + 5*\/ x / /   30*\-1 + \1 + 5*\/ x / /   3*\-1 + \1 + 5*\/ x / /      \       \1 + 5*\/ x /   /                                        \       \1 + 5*\/ x /   /                                 \       \1 + 5*\/ x /   / \                         x   *\1 + 5*\/ x /        x*\1 + 5*\/ x /     /                         |          60         6*\-1 + \1 + 5*\/ x / /   60*\-1 + \1 + 5*\/ x / /      \       \1 + 5*\/ x /   /                          |        ___ |       2|-1 + \1 + 5*\/ x / || |    -1 + \1 + 5*\/ x / ||    
|                                                          15*|1 + tan |-------------------||*|x*|- ---- - --------------- + ------------------- + ------------------------ + ------------------------------------------------------| + ---------------------------|   5*|1 + tan |-------------------||*|- ---- + x*|---- + ---------------- + ------------------- - ------------------------- - ------------------------ - ----------------------- + ------------------------------------------------------------- + -------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------| - --------------- + ----------------------- + ------------------------ + ------------------------------------------------------|   15*\/ x *|1 + tan |-------------------||*|2 - -------------------||    
|     /                  2\        /                  2\      |        |            ___    || |  |   3/2     /        ___\                     2                      3                                 x                           |                ___           |     |        |            ___    || |   3/2     | 5/2    2 /        ___\                     2                        4                         3                           2                                   3/2                                                          3/2                                                                                            ___                                                             |     /        ___\                       2                        3                                 x                           |            |        |            ___    || |                    2  ||    
|     |     /        ___\ |        |     /        ___\ |      \        \    1 + 5*\/ x     // |  |  x      x*\1 + 5*\/ x /    3/2 /        ___\          /        ___\                                                              |              \/ x            |     \        \    1 + 5*\/ x     // |  x        |x      x *\1 + 5*\/ x /    3/2 /        ___\        3/2 /        ___\           2 /        ___\           5/2 /        ___\                                   x                                                            x                                                                                             \/ x                                                              |   x*\1 + 5*\/ x /      3/2 /        ___\            /        ___\                                                              |            \        \    1 + 5*\/ x     // |       /        ___\   ||    
|     |-1 + \1 + 5*\/ x / |        |-1 + \1 + 5*\/ x / |                                      \  \                           x   *\1 + 5*\/ x /        x*\1 + 5*\/ x /                                                              /                              /                                     \           \                          x   *\1 + 5*\/ x /       x   *\1 + 5*\/ x /          x *\1 + 5*\/ x /          x   *\1 + 5*\/ x /                                                                                                                                                                                                                                                                /                       x   *\1 + 5*\/ x /          x*\1 + 5*\/ x /                                                              /                                            \       \1 + 5*\/ x /   /|  -x
|3*tan|-------------------| - x*tan|-------------------| - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------|*e  
|     |            ___    |        |            ___    |                                                                                                       4                                                                                                                                                                                                                                                                                                                                                                                            8                                                                                                                                                                                                                                                                                                                         2                                 |    
\     \    1 + 5*\/ x     /        \    1 + 5*\/ x     /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /
(15x(2−(5x+1)2−1(5x+1)2)(tan⁡2((5x+1)2−15x+1)+1)2−xtan⁡((5x+1)2−15x+1)−15(x(10(2−(5x+1)2−1(5x+1)2)2tan⁡((5x+1)2−15x+1)x−10x(5x+1)+10((5x+1)2−1)x(5x+1)3−2x32+(5x+1)2−1x32(5x+1)2)+4(2−(5x+1)2−1(5x+1)2)x)(tan⁡2((5x+1)2−15x+1)+1)4+5(tan⁡2((5x+1)2−15x+1)+1)(x(30x2(5x+1)−30((5x+1)2−1)x2(5x+1)3−30(2−(5x+1)2−1(5x+1)2)(10x(5x+1)−10((5x+1)2−1)x(5x+1)3+2x32−(5x+1)2−1x32(5x+1)2)tan⁡((5x+1)2−15x+1)x+50(2−(5x+1)2−1(5x+1)2)3(tan⁡2((5x+1)2−15x+1)+1)x32+100(2−(5x+1)2−1(5x+1)2)3tan⁡2((5x+1)2−15x+1)x32+150x32(5x+1)2−150((5x+1)2−1)x32(5x+1)4+6x52−3((5x+1)2−1)x52(5x+1)2)+60(2−(5x+1)2−1(5x+1)2)2tan⁡((5x+1)2−15x+1)x−60x(5x+1)+60((5x+1)2−1)x(5x+1)3−12x32+6((5x+1)2−1)x32(5x+1)2)8+3tan⁡((5x+1)2−15x+1))e−x\left(\frac{15 \sqrt{x} \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{2} - x \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} - \frac{15 \left(x \left(\frac{10 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{2} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x} - \frac{10}{x \left(5 \sqrt{x} + 1\right)} + \frac{10 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} - \frac{2}{x^{\frac{3}{2}}} + \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) + \frac{4 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)}{\sqrt{x}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{4} + \frac{5 \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right) \left(x \left(\frac{30}{x^{2} \left(5 \sqrt{x} + 1\right)} - \frac{30 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{2} \left(5 \sqrt{x} + 1\right)^{3}} - \frac{30 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\frac{10}{x \left(5 \sqrt{x} + 1\right)} - \frac{10 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} + \frac{2}{x^{\frac{3}{2}}} - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{\sqrt{x}} + \frac{50 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{3} \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{100 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{3} \tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x^{\frac{3}{2}}} + \frac{150}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}} - \frac{150 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{4}} + \frac{6}{x^{\frac{5}{2}}} - \frac{3 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{\frac{5}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) + \frac{60 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{2} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x} - \frac{60}{x \left(5 \sqrt{x} + 1\right)} + \frac{60 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} - \frac{12}{x^{\frac{3}{2}}} + \frac{6 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right)}{8} + 3 \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}\right) e^{- x}
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Gráfico
Derivada de xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))*exp(-x)
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