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y=((2ctg2x-3tg3x))*arcsin((x+1)/(x+2))
Derivada de la función/ y=((2ctg2x-3tg3x))*arcsin((x+1)/(x+2))

Derivada de y=((2ctg2x-3tg3x))*arcsin((x+1)/(x+2))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
                              /x + 1\
(2*cot(2*x) - 3*tan(3*x))*asin|-----|
                              \x + 2/
(−3tan⁡(3x)+2cot⁡(2x))asin⁡(x+1x+2)\left(- 3 \tan{\left(3 x \right)} + 2 \cot{\left(2 x \right)}\right) \operatorname{asin}{\left(\frac{x + 1}{x + 2} \right)} 
(2*cot(2*x) - 3*tan(3*x))*asin((x + 1)/(x + 2))
Gráfica
02468-8-6-4-2-1010-500000250000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                                /  1      x + 1  \                          
                                                |----- - --------|*(2*cot(2*x) - 3*tan(3*x))
                                                |x + 2          2|                          
/           2             2     \     /x + 1\   \        (x + 2) /                          
\-13 - 9*tan (3*x) - 4*cot (2*x)/*asin|-----| + --------------------------------------------
                                      \x + 2/                     ______________            
                                                                 /            2             
                                                                /      (x + 1)              
                                                               /   1 - --------             
                                                              /               2             
                                                            \/         (x + 2)
(−x+1(x+2)2+1x+2)(−3tan⁡(3x)+2cot⁡(2x))−(x+1)2(x+2)2+1+(−9tan⁡2(3x)−4cot⁡2(2x)−13)asin⁡(x+1x+2)\frac{\left(- \frac{x + 1}{\left(x + 2\right)^{2}} + \frac{1}{x + 2}\right) \left(- 3 \tan{\left(3 x \right)} + 2 \cot{\left(2 x \right)}\right)}{\sqrt{- \frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} + 1}} + \left(- 9 \tan^{2}{\left(3 x \right)} - 4 \cot^{2}{\left(2 x \right)} - 13\right) \operatorname{asin}{\left(\frac{x + 1}{x + 2} \right)}
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Segunda derivada [src] 
                                                                                                                                              /               /     1 + x\ \                           
                                                                                                                                              |       (1 + x)*|-1 + -----| |                           
                                                                                                                                 /     1 + x\ |               \     2 + x/ |                           
                                                                                                                                 |-1 + -----|*|-2 + -----------------------|*(-2*cot(2*x) + 3*tan(3*x))
                                                                                                                                 \     2 + x/ |     /            2\        |                           
                                                                                                                                              |     |     (1 + x) |        |                           
                                                                                 /     1 + x\ /          2             2     \                |     |-1 + --------|*(2 + x)|                           
                                                                               2*|-1 + -----|*\13 + 4*cot (2*x) + 9*tan (3*x)/                |     |            2|        |                           
    /    /       2     \               /       2     \         \     /1 + x\     \     2 + x/                                                 \     \     (2 + x) /        /                           
- 2*\- 8*\1 + cot (2*x)/*cot(2*x) + 27*\1 + tan (3*x)/*tan(3*x)/*asin|-----| + ----------------------------------------------- + ----------------------------------------------------------------------
                                                                     \2 + x/                   ______________                                              ______________                              
                                                                                              /            2                                              /            2                               
                                                                                             /      (1 + x)                                              /      (1 + x)          2                     
                                                                                            /   1 - -------- *(2 + x)                                   /   1 - -------- *(2 + x)                      
                                                                                           /               2                                           /               2                               
                                                                                         \/         (2 + x)                                          \/         (2 + x)
−2(27(tan⁡2(3x)+1)tan⁡(3x)−8(cot⁡2(2x)+1)cot⁡(2x))asin⁡(x+1x+2)+2(x+1x+2−1)(9tan⁡2(3x)+4cot⁡2(2x)+13)(x+2)−(x+1)2(x+2)2+1+(x+1x+2−1)((x+1)(x+1x+2−1)(x+2)((x+1)2(x+2)2−1)−2)(3tan⁡(3x)−2cot⁡(2x))(x+2)2−(x+1)2(x+2)2+1- 2 \left(27 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)} - 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}\right) \operatorname{asin}{\left(\frac{x + 1}{x + 2} \right)} + \frac{2 \left(\frac{x + 1}{x + 2} - 1\right) \left(9 \tan^{2}{\left(3 x \right)} + 4 \cot^{2}{\left(2 x \right)} + 13\right)}{\left(x + 2\right) \sqrt{- \frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} + 1}} + \frac{\left(\frac{x + 1}{x + 2} - 1\right) \left(\frac{\left(x + 1\right) \left(\frac{x + 1}{x + 2} - 1\right)}{\left(x + 2\right) \left(\frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} - 1\right)} - 2\right) \left(3 \tan{\left(3 x \right)} - 2 \cot{\left(2 x \right)}\right)}{\left(x + 2\right)^{2} \sqrt{- \frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} + 1}}
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Tercera derivada [src] 
                                                                                                                                                                                                                                                   /                             2                                                      \                                                                                 
                                                                                                                                                                                                                                                   |        4*(1 + x)   3*(1 + x)                                                      2|                                                                                 
                                                                                                                                                                                                                                                   |    1 - --------- + ----------              /     1 + x\             2 /     1 + x\ |                                                                                 
                                                                                                                                                                                                                                                   |          2 + x             2     4*(1 + x)*|-1 + -----|    3*(1 + x) *|-1 + -----| |                  /               /     1 + x\ \                                 
                                                                                                                                                                                                           /     1 + x\                            |                     (2 + x)                \     2 + x/               \     2 + x/ |                  |       (1 + x)*|-1 + -----| |                                 
                                                                                                                                                                                                           |-1 + -----|*(-2*cot(2*x) + 3*tan(3*x))*|6 - -------------------------- - ----------------------- + -------------------------|     /     1 + x\ |               \     2 + x/ | /          2             2     \
                                                                                                                                                                                                           \     2 + x/                            |                      2          /            2\                          2         |   3*|-1 + -----|*|-2 + -----------------------|*\13 + 4*cot (2*x) + 9*tan (3*x)/
                                                                                                                                                                                                                                                   |               (1 + x)           |     (1 + x) |           /            2\          |     \     2 + x/ |     /            2\        |                                 
                                                                                                                                                                                                                                                   |          -1 + --------          |-1 + --------|*(2 + x)   |     (1 + x) |         2|                  |     |     (1 + x) |        |                                 
                                                                                                                               /     1 + x\ /    /       2     \               /       2     \         \                                           |                      2          |            2|           |-1 + --------| *(2 + x) |                  |     |-1 + --------|*(2 + x)|                                 
    /                  2                     2                                                               \               6*|-1 + -----|*\- 8*\1 + cot (2*x)/*cot(2*x) + 27*\1 + tan (3*x)/*tan(3*x)/                                           |               (2 + x)           \     (2 + x) /           |            2|          |                  |     |            2|        |                                 
    |   /       2     \       /       2     \          2      /       2     \          2      /       2     \|     /1 + x\     \     2 + x/                                                                                                        \                                                           \     (2 + x) /          /                  \     \     (2 + x) /        /                                 
- 2*\16*\1 + cot (2*x)/  + 81*\1 + tan (3*x)/  + 32*cot (2*x)*\1 + cot (2*x)/ + 162*tan (3*x)*\1 + tan (3*x)//*asin|-----| + --------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------
                                                                                                                   \2 + x/                                 ______________                                                                                        ______________                                                                                           ______________                                  
                                                                                                                                                          /            2                                                                                        /            2                                                                                           /            2                                   
                                                                                                                                                         /      (1 + x)                                                                                        /      (1 + x)          3                                                                                /      (1 + x)          2                         
                                                                                                                                                        /   1 - -------- *(2 + x)                                                                             /   1 - -------- *(2 + x)                                                                                /   1 - -------- *(2 + x)                          
                                                                                                                                                       /               2                                                                                     /               2                                                                                        /               2                                   
                                                                                                                                                     \/         (2 + x)                                                                                    \/         (2 + x)                                                                                       \/         (2 + x)
−2(81(tan⁡2(3x)+1)2+162(tan⁡2(3x)+1)tan⁡2(3x)+16(cot⁡2(2x)+1)2+32(cot⁡2(2x)+1)cot⁡2(2x))asin⁡(x+1x+2)+6(x+1x+2−1)(27(tan⁡2(3x)+1)tan⁡(3x)−8(cot⁡2(2x)+1)cot⁡(2x))(x+2)−(x+1)2(x+2)2+1+3(x+1x+2−1)((x+1)(x+1x+2−1)(x+2)((x+1)2(x+2)2−1)−2)(9tan⁡2(3x)+4cot⁡2(2x)+13)(x+2)2−(x+1)2(x+2)2+1+(x+1x+2−1)(3tan⁡(3x)−2cot⁡(2x))(3(x+1)2(x+1x+2−1)2(x+2)2((x+1)2(x+2)2−1)2−4(x+1)(x+1x+2−1)(x+2)((x+1)2(x+2)2−1)+6−3(x+1)2(x+2)2−4(x+1)x+2+1(x+1)2(x+2)2−1)(x+2)3−(x+1)2(x+2)2+1- 2 \left(81 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} + 162 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan^{2}{\left(3 x \right)} + 16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} + 32 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot^{2}{\left(2 x \right)}\right) \operatorname{asin}{\left(\frac{x + 1}{x + 2} \right)} + \frac{6 \left(\frac{x + 1}{x + 2} - 1\right) \left(27 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)} - 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}\right)}{\left(x + 2\right) \sqrt{- \frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} + 1}} + \frac{3 \left(\frac{x + 1}{x + 2} - 1\right) \left(\frac{\left(x + 1\right) \left(\frac{x + 1}{x + 2} - 1\right)}{\left(x + 2\right) \left(\frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} - 1\right)} - 2\right) \left(9 \tan^{2}{\left(3 x \right)} + 4 \cot^{2}{\left(2 x \right)} + 13\right)}{\left(x + 2\right)^{2} \sqrt{- \frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} + 1}} + \frac{\left(\frac{x + 1}{x + 2} - 1\right) \left(3 \tan{\left(3 x \right)} - 2 \cot{\left(2 x \right)}\right) \left(\frac{3 \left(x + 1\right)^{2} \left(\frac{x + 1}{x + 2} - 1\right)^{2}}{\left(x + 2\right)^{2} \left(\frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} - 1\right)^{2}} - \frac{4 \left(x + 1\right) \left(\frac{x + 1}{x + 2} - 1\right)}{\left(x + 2\right) \left(\frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} - 1\right)} + 6 - \frac{\frac{3 \left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} - \frac{4 \left(x + 1\right)}{x + 2} + 1}{\frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} - 1}\right)}{\left(x + 2\right)^{3} \sqrt{- \frac{\left(x + 1\right)^{2}}{\left(x + 2\right)^{2}} + 1}}
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Gráfico
Derivada de y=((2ctg2x-3tg3x))*arcsin((x+1)/(x+2))
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