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y=(tg(cos(ln2+x))*(2x+2^2))/(tg(x+e^sqrt(2x)))
Derivada de la función/ y=(tg(cos(ln2+x))*(2x+2^2))/(tg(x+e^sqrt(2x)))

Derivada de y=(tg(cos(ln2+x))*(2x+2^2))/(tg(x+e^sqrt(2x)))

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

Gráfico:

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Solución

Ha introducido [src] 
tan(cos(log(2) + x))*(2*x + 4)
------------------------------
         /       _____\       
         |     \/ 2*x |       
      tan\x + E       /
(2x+4)tan⁡(cos⁡(x+log⁡(2)))tan⁡(e2x+x)\frac{\left(2 x + 4\right) \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}}{\tan{\left(e^{\sqrt{2 x}} + x \right)}} 
(tan(cos(log(2) + x))*(2*x + 4))/tan(x + E^(sqrt(2*x)))
Gráfica
02468-8-6-4-2-1010-100000100000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                                                                                          /             _____\                               
                                                                                 /        /       _____\\ |      ___  \/ 2*x |                               
                                                                                 |       2|     \/ 2*x || |    \/ 2 *e       |                               
                                                                                 \1 + tan \x + E       //*|1 + --------------|*(2*x + 4)*tan(cos(log(2) + x))
                         /       2                 \                                                      |           ___    |                               
2*tan(cos(log(2) + x)) - \1 + tan (cos(log(2) + x))/*(2*x + 4)*sin(log(2) + x)                            \       2*\/ x     /                               
------------------------------------------------------------------------------ - ----------------------------------------------------------------------------
                                 /       _____\                                                                   /       _____\                             
                                 |     \/ 2*x |                                                                  2|     \/ 2*x |                             
                              tan\x + E       /                                                               tan \x + E       /
−(1+2e2x2x)(2x+4)(tan⁡2(e2x+x)+1)tan⁡(cos⁡(x+log⁡(2)))tan⁡2(e2x+x)+−(2x+4)(tan⁡2(cos⁡(x+log⁡(2)))+1)sin⁡(x+log⁡(2))+2tan⁡(cos⁡(x+log⁡(2)))tan⁡(e2x+x)- \frac{\left(1 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{2 \sqrt{x}}\right) \left(2 x + 4\right) \left(\tan^{2}{\left(e^{\sqrt{2 x}} + x \right)} + 1\right) \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}}{\tan^{2}{\left(e^{\sqrt{2 x}} + x \right)}} + \frac{- \left(2 x + 4\right) \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right) \sin{\left(x + \log{\left(2 \right)} \right)} + 2 \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}}{\tan{\left(e^{\sqrt{2 x}} + x \right)}}
Simplificar
Segunda derivada [src] 
                                                                                                                                                                                                                                                                                                     /                                                                        2                             \                     
                                                                                                                                                                                                                                                                                                     |                                                    /             _____\                              |                     
                                                                                                                                                                                                                                                                                                     |                           /      ___\    _____     |      ___  \/ 2*x |  /        /       ___   ___\\|                     
                                                                                                                                                                                                                                                                                                     |                      2    |2   \/ 2 |  \/ 2*x      |    \/ 2 *e       |  |       2|     \/ 2 *\/ x |||                     
                                                                                                                                                                                                                                                                                                     |  /             _____\     |- - -----|*e          2*|2 + --------------| *\1 + tan \x + e           //|                     
                                                                                                                                                           /             _____\                                                                                 /        /       ___   ___\\         |  |      ___  \/ 2*x |     |x     3/2|              |          ___     |                              |                     
                                                                                                                              /        /       ___   ___\\ |      ___  \/ 2*x |                                                                                 |       2|     \/ 2 *\/ x ||         |  |    \/ 2 *e       |     \     x   /              \        \/ x      /                              |                     
                                                                                                                              |       2|     \/ 2 *\/ x || |    \/ 2 *e       | /                        /       2                 \                        \   \1 + tan \x + e           //*(2 + x)*|2*|2 + --------------|  + --------------------- - ----------------------------------------------------|*tan(cos(x + log(2)))
                                                                                                                            2*\1 + tan \x + e           //*|2 + --------------|*\-tan(cos(x + log(2))) + \1 + tan (cos(x + log(2)))/*(2 + x)*sin(x + log(2))/                                        |  |          ___     |       /       ___   ___\                      /       ___   ___\               |                     
                                                                                                                                                           |          ___     |                                                                                                                      |  \        \/ x      /       |     \/ 2 *\/ x |                     2|     \/ 2 *\/ x |               |                     
  /       2                 \ /                             /                        2                                 \\                                  \        \/ x      /                                                                                                                      \                          tan\x + e           /                  tan \x + e           /               /                     
2*\1 + tan (cos(x + log(2)))/*\-2*sin(x + log(2)) + (2 + x)*\-cos(x + log(2)) + 2*sin (x + log(2))*tan(cos(x + log(2)))// + --------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                     /       ___   ___\                                                                                                                                         2                                                                                 
                                                                                                                                                                                     |     \/ 2 *\/ x |                                                                                                                                                                                                                           
                                                                                                                                                                                  tan\x + e           /                                                                                                                                                                                                                           
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                         /       ___   ___\                                                                                                                                                                                                       
                                                                                                                                                                                                         |     \/ 2 *\/ x |                                                                                                                                                                                                       
                                                                                                                                                                                                      tan\x + e           /
2(2+2e2xx)((x+2)(tan⁡2(cos⁡(x+log⁡(2)))+1)sin⁡(x+log⁡(2))−tan⁡(cos⁡(x+log⁡(2))))(tan⁡2(x+e2x)+1)tan⁡(x+e2x)−(x+2)(tan⁡2(x+e2x)+1)(−2(2+2e2xx)2(tan⁡2(x+e2x)+1)tan⁡2(x+e2x)+2(2+2e2xx)2+(2x−2x32)e2xtan⁡(x+e2x))tan⁡(cos⁡(x+log⁡(2)))2+2((x+2)(2sin⁡2(x+log⁡(2))tan⁡(cos⁡(x+log⁡(2)))−cos⁡(x+log⁡(2)))−2sin⁡(x+log⁡(2)))(tan⁡2(cos⁡(x+log⁡(2)))+1)tan⁡(x+e2x)\frac{\frac{2 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right) \left(\left(x + 2\right) \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right) \sin{\left(x + \log{\left(2 \right)} \right)} - \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}\right) \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right)}{\tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} - \frac{\left(x + 2\right) \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right) \left(- \frac{2 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{2} \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right)}{\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} + 2 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{2} + \frac{\left(\frac{2}{x} - \frac{\sqrt{2}}{x^{\frac{3}{2}}}\right) e^{\sqrt{2 x}}}{\tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}}\right) \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}}{2} + 2 \left(\left(x + 2\right) \left(2 \sin^{2}{\left(x + \log{\left(2 \right)} \right)} \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} - \cos{\left(x + \log{\left(2 \right)} \right)}\right) - 2 \sin{\left(x + \log{\left(2 \right)} \right)}\right) \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right)}{\tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                                                                                                                                                         /                                                                                       3                                                                                    3                                                                                                                         \                                                                                                                                     /                                                                        2                             \                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                         |                                                                   /             _____\                                                               2 /             _____\      /             _____\                                                       /             _____\                     |                                                                                                                                     |                                                    /             _____\                              |                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                         |                          /           ___       ___\    _____      |      ___  \/ 2*x |  /        /       ___   ___\\     /        /       ___   ___\\  |      ___  \/ 2*x |      |      ___  \/ 2*x | /      ___\    _____     /        /       ___   ___\\ |      ___  \/ 2*x | /      ___\    _____|                                                                                                                                     |                           /      ___\    _____     |      ___  \/ 2*x |  /        /       ___   ___\\|                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                         |                      3   |  6    2*\/ 2    3*\/ 2 |  \/ 2*x       |    \/ 2 *e       |  |       2|     \/ 2 *\/ x ||     |       2|     \/ 2 *\/ x ||  |    \/ 2 *e       |      |    \/ 2 *e       | |2   \/ 2 |  \/ 2*x      |       2|     \/ 2 *\/ x || |    \/ 2 *e       | |2   \/ 2 |  \/ 2*x |                                                                                                                                     |                      2    |2   \/ 2 |  \/ 2*x      |    \/ 2 *e       |  |       2|     \/ 2 *\/ x |||                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                         |  /             _____\    |- -- + ------- + -------|*e          10*|2 + --------------| *\1 + tan \x + e           //   6*\1 + tan \x + e           // *|2 + --------------|    6*|2 + --------------|*|- - -----|*e          6*\1 + tan \x + e           //*|2 + --------------|*|- - -----|*e       |                                                                                                                                     |  /             _____\     |- - -----|*e          2*|2 + --------------| *\1 + tan \x + e           //|                                                                                                                                                                              
                                                                                                                                                                                                                                                                    /        /       ___   ___\\         |  |      ___  \/ 2*x |    |   2      3/2       5/2 |               |          ___     |                                                                 |          ___     |      |          ___     | |x     3/2|                                           |          ___     | |x     3/2|         |                          /        /       ___   ___\\                                                                               |  |      ___  \/ 2*x |     |x     3/2|              |          ___     |                              |                                                              /             _____\                                                                                            
                                                                                                                                                                                                                                                                    |       2|     \/ 2 *\/ x ||         |  |    \/ 2 *e       |    \  x      x         x    /               \        \/ x      /                                                                 \        \/ x      /      \        \/ x      / \     x   /                                           \        \/ x      / \     x   /         |                          |       2|     \/ 2 *\/ x || /                        /       2                 \                        \ |  |    \/ 2 *e       |     \     x   /              \        \/ x      /                              |     /        /       ___   ___\\                             |      ___  \/ 2*x |                                                                                            
                                                                                                                                                                                                                                                                    \1 + tan \x + e           //*(2 + x)*|4*|2 + --------------|  + ----------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------- - ------------------------------------------------------------------------|*tan(cos(x + log(2)))   3*\1 + tan \x + e           //*\-tan(cos(x + log(2))) + \1 + tan (cos(x + log(2)))/*(2 + x)*sin(x + log(2))/*|2*|2 + --------------|  + --------------------- - ----------------------------------------------------|     |       2|     \/ 2 *\/ x || /       2                 \ |    \/ 2 *e       | /                             /                        2                                 \\
                                                                                                                                                                                                                                                                                                         |  |          ___     |               /       ___   ___\                             /       ___   ___\                                      /       ___   ___\                                /       ___   ___\                                           /       ___   ___\                         |                                                                                                                                     |  |          ___     |       /       ___   ___\                      /       ___   ___\               |   3*\1 + tan \x + e           //*\1 + tan (cos(x + log(2)))/*|2 + --------------|*\-2*sin(x + log(2)) + (2 + x)*\-cos(x + log(2)) + 2*sin (x + log(2))*tan(cos(x + log(2)))//
    /       2                 \ /                         2                                            /                                                   2             /       2                 \        2                2                 \                \                                        |  \        \/ x      /              2|     \/ 2 *\/ x |                            2|     \/ 2 *\/ x |                                     4|     \/ 2 *\/ x |                                |     \/ 2 *\/ x |                                          3|     \/ 2 *\/ x |                         |                                                                                                                                     |  \        \/ x      /       |     \/ 2 *\/ x |                     2|     \/ 2 *\/ x |               |                                                              |          ___     |                                                                                            
  2*\1 + tan (cos(x + log(2)))/*\3*cos(x + log(2)) - 6*sin (x + log(2))*tan(cos(x + log(2))) + (2 + x)*\-1 - 6*cos(x + log(2))*tan(cos(x + log(2))) + 2*sin (x + log(2))*\1 + tan (cos(x + log(2)))/ + 4*sin (x + log(2))*tan (cos(x + log(2)))/*sin(x + log(2))/                                        \                                 tan \x + e           /                         tan \x + e           /                                  tan \x + e           /                             tan\x + e           /                                       tan \x + e           /                         /                                                                                                                                     \                          tan\x + e           /                  tan \x + e           /               /                                                              \        \/ x      /                                                                                            
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                                                                                                                          |     \/ 2 *\/ x |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |     \/ 2 *\/ x |                                                                                                                                                                                2|     \/ 2 *\/ x |                                                                          
                                                                                                                       tan\x + e           /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2*tan\x + e           /                                                                                                                                                                             tan \x + e           /
−3(2+2e2xx)((x+2)(2sin⁡2(x+log⁡(2))tan⁡(cos⁡(x+log⁡(2)))−cos⁡(x+log⁡(2)))−2sin⁡(x+log⁡(2)))(tan⁡2(x+e2x)+1)(tan⁡2(cos⁡(x+log⁡(2)))+1)tan⁡2(x+e2x)−(x+2)(tan⁡2(x+e2x)+1)(6(2+2e2xx)3(tan⁡2(x+e2x)+1)2tan⁡4(x+e2x)−10(2+2e2xx)3(tan⁡2(x+e2x)+1)tan⁡2(x+e2x)+4(2+2e2xx)3−6(2+2e2xx)(2x−2x32)(tan⁡2(x+e2x)+1)e2xtan⁡3(x+e2x)+6(2+2e2xx)(2x−2x32)e2xtan⁡(x+e2x)+(−6x2+22x32+32x52)e2xtan⁡2(x+e2x))tan⁡(cos⁡(x+log⁡(2)))4+3((x+2)(tan⁡2(cos⁡(x+log⁡(2)))+1)sin⁡(x+log⁡(2))−tan⁡(cos⁡(x+log⁡(2))))(tan⁡2(x+e2x)+1)(−2(2+2e2xx)2(tan⁡2(x+e2x)+1)tan⁡2(x+e2x)+2(2+2e2xx)2+(2x−2x32)e2xtan⁡(x+e2x))2tan⁡(x+e2x)−2(tan⁡2(cos⁡(x+log⁡(2)))+1)((x+2)(2(tan⁡2(cos⁡(x+log⁡(2)))+1)sin⁡2(x+log⁡(2))+4sin⁡2(x+log⁡(2))tan⁡2(cos⁡(x+log⁡(2)))−6cos⁡(x+log⁡(2))tan⁡(cos⁡(x+log⁡(2)))−1)sin⁡(x+log⁡(2))−6sin⁡2(x+log⁡(2))tan⁡(cos⁡(x+log⁡(2)))+3cos⁡(x+log⁡(2)))tan⁡(x+e2x)- \frac{3 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right) \left(\left(x + 2\right) \left(2 \sin^{2}{\left(x + \log{\left(2 \right)} \right)} \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} - \cos{\left(x + \log{\left(2 \right)} \right)}\right) - 2 \sin{\left(x + \log{\left(2 \right)} \right)}\right) \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right) \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right)}{\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} - \frac{\left(x + 2\right) \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right) \left(\frac{6 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{3} \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right)^{2}}{\tan^{4}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} - \frac{10 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{3} \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right)}{\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} + 4 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{3} - \frac{6 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right) \left(\frac{2}{x} - \frac{\sqrt{2}}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right) e^{\sqrt{2 x}}}{\tan^{3}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} + \frac{6 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right) \left(\frac{2}{x} - \frac{\sqrt{2}}{x^{\frac{3}{2}}}\right) e^{\sqrt{2 x}}}{\tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} + \frac{\left(- \frac{6}{x^{2}} + \frac{2 \sqrt{2}}{x^{\frac{3}{2}}} + \frac{3 \sqrt{2}}{x^{\frac{5}{2}}}\right) e^{\sqrt{2 x}}}{\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}}\right) \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}}{4} + \frac{3 \left(\left(x + 2\right) \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right) \sin{\left(x + \log{\left(2 \right)} \right)} - \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)}\right) \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right) \left(- \frac{2 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{2} \left(\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)} + 1\right)}{\tan^{2}{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} + 2 \left(2 + \frac{\sqrt{2} e^{\sqrt{2 x}}}{\sqrt{x}}\right)^{2} + \frac{\left(\frac{2}{x} - \frac{\sqrt{2}}{x^{\frac{3}{2}}}\right) e^{\sqrt{2 x}}}{\tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}}\right)}{2 \tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}} - \frac{2 \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right) \left(\left(x + 2\right) \left(2 \left(\tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 1\right) \sin^{2}{\left(x + \log{\left(2 \right)} \right)} + 4 \sin^{2}{\left(x + \log{\left(2 \right)} \right)} \tan^{2}{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} - 6 \cos{\left(x + \log{\left(2 \right)} \right)} \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} - 1\right) \sin{\left(x + \log{\left(2 \right)} \right)} - 6 \sin^{2}{\left(x + \log{\left(2 \right)} \right)} \tan{\left(\cos{\left(x + \log{\left(2 \right)} \right)} \right)} + 3 \cos{\left(x + \log{\left(2 \right)} \right)}\right)}{\tan{\left(x + e^{\sqrt{2} \sqrt{x}} \right)}}
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Gráfico
Derivada de y=(tg(cos(ln2+x))*(2x+2^2))/(tg(x+e^sqrt(2x)))
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