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x*sqrt((3*x-2)/(3*x+2))*tg(2*x^2-9)exp(-x)
Derivada de la función/ x*sqrt((3*x-2)/(3*x+2))*tg(2*x^2-9)exp(-x)

Derivada de x*sqrt((3*x-2)/(3*x+2))*tg(2*x^2-9)exp(-x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
      _________                  
     / 3*x - 2     /   2    \  -x
x*  /  ------- *tan\2*x  - 9/*e  
  \/   3*x + 2
x3x−23x+2tan⁡(2x2−9)e−xx \sqrt{\frac{3 x - 2}{3 x + 2}} \tan{\left(2 x^{2} - 9 \right)} e^{- x} 
((x*sqrt((3*x - 2)/(3*x + 2)))*tan(2*x^2 - 9))*exp(-x)
Gráfica
02468-8-6-4-2-1010-5000000050000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
//                      _________                                       \                                                        \                                        
||                     / 3*x - 2            /     3        3*(3*x - 2) \|                                                        |                                        
||                x*  /  ------- *(3*x + 2)*|----------- - ------------||                                                        |                                        
||    _________     \/   3*x + 2            |2*(3*x + 2)              2||                          _________                     |             _________                  
||   / 3*x - 2                              \              2*(3*x + 2) /|    /   2    \      2    / 3*x - 2  /       2/   2    \\|  -x        / 3*x - 2   -x    /   2    \
||  /  -------  + ------------------------------------------------------|*tan\2*x  - 9/ + 4*x *  /  ------- *\1 + tan \2*x  - 9//|*e   - x*  /  ------- *e  *tan\2*x  - 9/
\\\/   3*x + 2                           3*x - 2                        /                      \/   3*x + 2                      /         \/   3*x + 2
−x3x−23x+2e−xtan⁡(2x2−9)+(4x23x−23x+2(tan⁡2(2x2−9)+1)+(x3x−23x+2(3x+2)(−3(3x−2)2(3x+2)2+32(3x+2))3x−2+3x−23x+2)tan⁡(2x2−9))e−x- x \sqrt{\frac{3 x - 2}{3 x + 2}} e^{- x} \tan{\left(2 x^{2} - 9 \right)} + \left(4 x^{2} \sqrt{\frac{3 x - 2}{3 x + 2}} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) + \left(\frac{x \sqrt{\frac{3 x - 2}{3 x + 2}} \left(3 x + 2\right) \left(- \frac{3 \left(3 x - 2\right)}{2 \left(3 x + 2\right)^{2}} + \frac{3}{2 \left(3 x + 2\right)}\right)}{3 x - 2} + \sqrt{\frac{3 x - 2}{3 x + 2}}\right) \tan{\left(2 x^{2} - 9 \right)}\right) e^{- x}
Simplificar
Segunda derivada [src] 
               /                                                                                                                                                                                                                                             /         /                          -2 + 3*x\\               \    
               |                                                                                                                                                                                                                                             |         |                     -1 + --------||               |    
               |                   /         /     -2 + 3*x\\                                                                                                                                                 /         /     -2 + 3*x\\     /     -2 + 3*x\ |         |   2          2           2 + 3*x ||    /        2\|    
    __________ |                   |     3*x*|-1 + --------||                                                                                                                                                 |     3*x*|-1 + --------||   3*|-1 + --------|*|-4 + 3*x*|-------- + ------- + -------------||*tan\-9 + 2*x /|    
   / -2 + 3*x  |     /        2\   |         \     2 + 3*x /|    /        2\      2 /       2/        2\\       /       2/        2\      2 /       2/        2\\    /        2\\       /       2/        2\\ |         \     2 + 3*x /|     \     2 + 3*x / \         \-2 + 3*x   2 + 3*x      -2 + 3*x  //               |  -x
  /  -------- *|x*tan\-9 + 2*x / + |-2 + -------------------|*tan\-9 + 2*x / - 8*x *\1 + tan \-9 + 2*x // + 4*x*\1 + tan \-9 + 2*x / + 8*x *\1 + tan \-9 + 2*x //*tan\-9 + 2*x // - 4*x*\1 + tan \-9 + 2*x //*|-2 + -------------------| + --------------------------------------------------------------------------------|*e  
\/   2 + 3*x   \                   \           -2 + 3*x     /                                                                                                                                                 \           -2 + 3*x     /                                     4*(-2 + 3*x)                                  /
3x−23x+2(−8x2(tan⁡2(2x2−9)+1)−4x(3x(3x−23x+2−1)3x−2−2)(tan⁡2(2x2−9)+1)+4x(8x2(tan⁡2(2x2−9)+1)tan⁡(2x2−9)+tan⁡2(2x2−9)+1)+xtan⁡(2x2−9)+(3x(3x−23x+2−1)3x−2−2)tan⁡(2x2−9)+3(3x(23x+2+3x−23x+2−13x−2+23x−2)−4)(3x−23x+2−1)tan⁡(2x2−9)4(3x−2))e−x\sqrt{\frac{3 x - 2}{3 x + 2}} \left(- 8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) - 4 x \left(\frac{3 x \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{3 x - 2} - 2\right) \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) + 4 x \left(8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) \tan{\left(2 x^{2} - 9 \right)} + \tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) + x \tan{\left(2 x^{2} - 9 \right)} + \left(\frac{3 x \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{3 x - 2} - 2\right) \tan{\left(2 x^{2} - 9 \right)} + \frac{3 \left(3 x \left(\frac{2}{3 x + 2} + \frac{\frac{3 x - 2}{3 x + 2} - 1}{3 x - 2} + \frac{2}{3 x - 2}\right) - 4\right) \left(\frac{3 x - 2}{3 x + 2} - 1\right) \tan{\left(2 x^{2} - 9 \right)}}{4 \left(3 x - 2\right)}\right) e^{- x}
Simplificar
Tercera derivada [src] 
               /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /                       /                                          2                                                                  \                    \                                                                                                           \    
               |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                       |                           /     -2 + 3*x\      /     -2 + 3*x\                             /     -2 + 3*x\  |     /     -2 + 3*x\|                                                                                                           |    
               |                                                                                                                                                                                                                               /         /     -2 + 3*x\\                                                                                                                                                                                                 /         /                          -2 + 3*x\\                                     |                       |                           |-1 + --------|    6*|-1 + --------|                           6*|-1 + --------|  |   2*|-1 + --------||                                                            /         /                          -2 + 3*x\\|    
               |                                                                                                                                                                                                                               |     3*x*|-1 + --------||                                                                                                                                                                                                 |         |                     -1 + --------||                     /     -2 + 3*x\ |   4          4        |     8            8        \     2 + 3*x /      \     2 + 3*x /            8                \     2 + 3*x /  |     \     2 + 3*x /|    /        2\                                             |         |                     -1 + --------|||    
               |                                                                                                /         /     -2 + 3*x\\                                                                                                     |         \     2 + 3*x /|    /        2\                              /         /     -2 + 3*x\\                                                                                                          /     -2 + 3*x\ |         |   2          2           2 + 3*x ||    /        2\   27*|-1 + --------|*|-------- + ------- - x*|----------- + ---------- + ---------------- + ----------------- + -------------------- + --------------------| + -----------------|*tan\-9 + 2*x /       /       2/        2\\ /     -2 + 3*x\ |         |   2          2           2 + 3*x |||    
    __________ |                                                                                                |     3*x*|-1 + --------||                                                                                                   3*|-2 + -------------------|*tan\-9 + 2*x /                              |     3*x*|-1 + --------||                                                                                                        9*|-1 + --------|*|-4 + 3*x*|-------- + ------- + -------------||*tan\-9 + 2*x /      \     2 + 3*x / |-2 + 3*x   2 + 3*x     |          2            2               2                   2      (-2 + 3*x)*(2 + 3*x)   (-2 + 3*x)*(2 + 3*x)|        -2 + 3*x    |                  9*x*\1 + tan \-9 + 2*x //*|-1 + --------|*|-4 + 3*x*|-------- + ------- + -------------|||    
   / -2 + 3*x  |       /        2\        /       2/        2\      2 /       2/        2\\    /        2\\     |         \     2 + 3*x /| /       2/        2\      2 /       2/        2\\    /        2\\       2 /       2/        2\\     \           -2 + 3*x     /                       /       2/        2\\ |         \     2 + 3*x /|       2 /       2/        2\\ /     /        2\      2 /       2/        2\\      2    2/        2\\     \     2 + 3*x / \         \-2 + 3*x   2 + 3*x      -2 + 3*x  //                                     \                       \(-2 + 3*x)    (2 + 3*x)      (-2 + 3*x)          (-2 + 3*x)                                                  /                    /                                            \     2 + 3*x / \         \-2 + 3*x   2 + 3*x      -2 + 3*x  //|  -x
  /  -------- *|- x*tan\-9 + 2*x / - 12*x*\1 + tan \-9 + 2*x / + 8*x *\1 + tan \-9 + 2*x //*tan\-9 + 2*x // - 6*|-2 + -------------------|*\1 + tan \-9 + 2*x / + 8*x *\1 + tan \-9 + 2*x //*tan\-9 + 2*x // + 12*x *\1 + tan \-9 + 2*x // - ------------------------------------------- + 12*x*\1 + tan \-9 + 2*x //*|-2 + -------------------| + 32*x *\1 + tan \-9 + 2*x //*\3*tan\-9 + 2*x / + 4*x *\1 + tan \-9 + 2*x // + 8*x *tan \-9 + 2*x // - -------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------|*e  
\/   2 + 3*x   \                                                                                                \           -2 + 3*x     /                                                                                                                        2                                                   \           -2 + 3*x     /                                                                                                                                          4*(-2 + 3*x)                                                                                                                              8*(-2 + 3*x)                                                                                                                                     -2 + 3*x                                        /
3x−23x+2(32x2(tan⁡2(2x2−9)+1)(4x2(tan⁡2(2x2−9)+1)+8x2tan⁡2(2x2−9)+3tan⁡(2x2−9))+12x2(tan⁡2(2x2−9)+1)+12x(3x(3x−23x+2−1)3x−2−2)(tan⁡2(2x2−9)+1)−12x(8x2(tan⁡2(2x2−9)+1)tan⁡(2x2−9)+tan⁡2(2x2−9)+1)−xtan⁡(2x2−9)+9x(3x(23x+2+3x−23x+2−13x−2+23x−2)−4)(3x−23x+2−1)(tan⁡2(2x2−9)+1)3x−2−6(3x(3x−23x+2−1)3x−2−2)(8x2(tan⁡2(2x2−9)+1)tan⁡(2x2−9)+tan⁡2(2x2−9)+1)−3(3x(3x−23x+2−1)3x−2−2)tan⁡(2x2−9)2−9(3x(23x+2+3x−23x+2−13x−2+23x−2)−4)(3x−23x+2−1)tan⁡(2x2−9)4(3x−2)+27(3x−23x+2−1)(−x(8(3x+2)2+6(3x−23x+2−1)(3x−2)(3x+2)+8(3x−2)(3x+2)+(3x−23x+2−1)2(3x−2)2+6(3x−23x+2−1)(3x−2)2+8(3x−2)2)+43x+2+2(3x−23x+2−1)3x−2+43x−2)tan⁡(2x2−9)8(3x−2))e−x\sqrt{\frac{3 x - 2}{3 x + 2}} \left(32 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) \left(4 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) + 8 x^{2} \tan^{2}{\left(2 x^{2} - 9 \right)} + 3 \tan{\left(2 x^{2} - 9 \right)}\right) + 12 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) + 12 x \left(\frac{3 x \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{3 x - 2} - 2\right) \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) - 12 x \left(8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) \tan{\left(2 x^{2} - 9 \right)} + \tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) - x \tan{\left(2 x^{2} - 9 \right)} + \frac{9 x \left(3 x \left(\frac{2}{3 x + 2} + \frac{\frac{3 x - 2}{3 x + 2} - 1}{3 x - 2} + \frac{2}{3 x - 2}\right) - 4\right) \left(\frac{3 x - 2}{3 x + 2} - 1\right) \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right)}{3 x - 2} - 6 \left(\frac{3 x \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{3 x - 2} - 2\right) \left(8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) \tan{\left(2 x^{2} - 9 \right)} + \tan^{2}{\left(2 x^{2} - 9 \right)} + 1\right) - \frac{3 \left(\frac{3 x \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{3 x - 2} - 2\right) \tan{\left(2 x^{2} - 9 \right)}}{2} - \frac{9 \left(3 x \left(\frac{2}{3 x + 2} + \frac{\frac{3 x - 2}{3 x + 2} - 1}{3 x - 2} + \frac{2}{3 x - 2}\right) - 4\right) \left(\frac{3 x - 2}{3 x + 2} - 1\right) \tan{\left(2 x^{2} - 9 \right)}}{4 \left(3 x - 2\right)} + \frac{27 \left(\frac{3 x - 2}{3 x + 2} - 1\right) \left(- x \left(\frac{8}{\left(3 x + 2\right)^{2}} + \frac{6 \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{\left(3 x - 2\right) \left(3 x + 2\right)} + \frac{8}{\left(3 x - 2\right) \left(3 x + 2\right)} + \frac{\left(\frac{3 x - 2}{3 x + 2} - 1\right)^{2}}{\left(3 x - 2\right)^{2}} + \frac{6 \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{\left(3 x - 2\right)^{2}} + \frac{8}{\left(3 x - 2\right)^{2}}\right) + \frac{4}{3 x + 2} + \frac{2 \left(\frac{3 x - 2}{3 x + 2} - 1\right)}{3 x - 2} + \frac{4}{3 x - 2}\right) \tan{\left(2 x^{2} - 9 \right)}}{8 \left(3 x - 2\right)}\right) e^{- x}
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Gráfico
Derivada de x*sqrt((3*x-2)/(3*x+2))*tg(2*x^2-9)exp(-x)
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