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sqrt(((x+4)^3),5)/(((x-1)^2)*(x+3)^5)
Derivada de la función/ sqrt(((x+4)^3),5)/(((x-1)^2)*(x+3)^5)

Derivada de sqrt(((x+4)^3),5)/(((x-1)^2)*(x+3)^5)

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

Gráfico:

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Solución

Ha introducido [src] 
   __________
  /        3 
\/  (x + 4)  
-------------
 /        5 \
 | (x + 3)  |
 |----------|
 |/   1    \|
 ||--------||
 ||       2||
 \\(x - 1) //
11(x−−4)311(x−1)2(x−−3)5\frac{\sqrt{\frac{1}{\frac{1}{\left(x - -4\right)^{3}}}}}{\frac{1}{\frac{1}{\left(x - 1\right)^{2}}} \left(x - -3\right)^{5}} 
sqrt((x + 4)^3)/(((x + 3)^5/(x - 1)^(-2)))
Gráfica
02468-8-6-4-2-1010-50000005000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
     __________                                                                                
    /        3          1                                                                      
3*\/  (x + 4)  *-----------------      __________                                              
                       2        5     /        3  /         5                       2        4\
                (x - 1) *(x + 3)    \/  (x + 4)  *\- (x + 3) *(-2 + 2*x) - 5*(x - 1) *(x + 3) /
--------------------------------- + -----------------------------------------------------------
            2*(x + 4)                                           4        10                    
                                                         (x - 1) *(x + 3)
31(x−1)2(x+3)5(x−−4)32(x−−4)+(−5(x−1)2(x+3)4−(x+3)5(2x−2))(x−−4)3(x−1)4(x+3)10\frac{3 \frac{1}{\left(x - 1\right)^{2} \left(x + 3\right)^{5}} \sqrt{\left(x - -4\right)^{3}}}{2 \left(x - -4\right)} + \frac{\left(- 5 \left(x - 1\right)^{2} \left(x + 3\right)^{4} - \left(x + 3\right)^{5} \left(2 x - 2\right)\right) \sqrt{\left(x - -4\right)^{3}}}{\left(x - 1\right)^{4} \left(x + 3\right)^{10}}
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Segunda derivada [src] 
              /                                                                        /       2              2                      \                           \
              |                       /  2        5  \   2*(1 + 7*x)   5*(1 + 7*x)   2*\(3 + x)  + 10*(-1 + x)  + 10*(-1 + x)*(3 + x)/                           |
   __________ |             (1 + 7*x)*|------ + -----| + ----------- + ----------- - -------------------------------------------------                           |
  /        3  |    3                  \-1 + x   3 + x/      -1 + x        3 + x                       (-1 + x)*(3 + x)                         3*(1 + 7*x)       |
\/  (4 + x)  *|---------- + ---------------------------------------------------------------------------------------------------------- - ------------------------|
              |         2                                                (-1 + x)*(3 + x)                                                (-1 + x)*(3 + x)*(4 + x)|
              \4*(4 + x)                                                                                                                                         /
------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                2        5                                                                        
                                                                        (-1 + x) *(3 + x)
(34(x+4)2+(7x+1)(5x+3+2x−1)+5(7x+1)x+3+2(7x+1)x−1−2(10(x−1)2+10(x−1)(x+3)+(x+3)2)(x−1)(x+3)(x−1)(x+3)−3(7x+1)(x−1)(x+3)(x+4))(x+4)3(x−1)2(x+3)5\frac{\left(\frac{3}{4 \left(x + 4\right)^{2}} + \frac{\left(7 x + 1\right) \left(\frac{5}{x + 3} + \frac{2}{x - 1}\right) + \frac{5 \left(7 x + 1\right)}{x + 3} + \frac{2 \left(7 x + 1\right)}{x - 1} - \frac{2 \left(10 \left(x - 1\right)^{2} + 10 \left(x - 1\right) \left(x + 3\right) + \left(x + 3\right)^{2}\right)}{\left(x - 1\right) \left(x + 3\right)}}{\left(x - 1\right) \left(x + 3\right)} - \frac{3 \left(7 x + 1\right)}{\left(x - 1\right) \left(x + 3\right) \left(x + 4\right)}\right) \sqrt{\left(x + 4\right)^{3}}}{\left(x - 1\right)^{2} \left(x + 3\right)^{5}}
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Tercera derivada [src] 
              /                                                                                                                                                                                                                           /  2        5  \               /  2        5  \                                                                           /  2        5  \ /       2              2                      \                                                                                                                                               \
              |                                                                                                        /       2              2                      \      /       2              2                      \   2*(1 + 7*x)*|------ + -----|   5*(1 + 7*x)*|------ + -----|      /       2             2                     \                      2*|------ + -----|*\(3 + x)  + 10*(-1 + x)  + 10*(-1 + x)*(3 + x)/                                                                                                                                               |
              |                           /    3          15             10       \   10*(1 + 7*x)   55*(1 + 7*x)   30*\(3 + x)  + 10*(-1 + x)  + 10*(-1 + x)*(3 + x)/   12*\(3 + x)  + 10*(-1 + x)  + 10*(-1 + x)*(3 + x)/               \-1 + x   3 + x/               \-1 + x   3 + x/   30*\(3 + x)  + 2*(-1 + x)  + 4*(-1 + x)*(3 + x)/     40*(1 + 7*x)       \-1 + x   3 + x/                                                                                   /                                                           /       2              2                      \\|
              |               2*(1 + 7*x)*|--------- + -------- + ----------------| + ------------ + ------------ - -------------------------------------------------- - -------------------------------------------------- + ---------------------------- + ---------------------------- + ------------------------------------------------ + ---------------- - ------------------------------------------------------------------                                   |          /  2        5  \   2*(1 + 7*x)   5*(1 + 7*x)   2*\(3 + x)  + 10*(-1 + x)  + 10*(-1 + x)*(3 + x)/||
   __________ |                           |        2          2   (-1 + x)*(3 + x)|            2              2                                     2                                            2                                       -1 + x                         3 + x                                              2                   (-1 + x)*(3 + x)                            (-1 + x)*(3 + x)                                                          9*|(1 + 7*x)*|------ + -----| + ----------- + ----------- - -------------------------------------------------||
  /        3  |      3                    \(-1 + x)    (3 + x)                    /    (-1 + x)        (3 + x)                      (-1 + x)*(3 + x)                                     (-1 + x) *(3 + x)                                                                                                 (-1 + x)*(3 + x)                                                                                                                    9*(1 + 7*x)             \          \-1 + x   3 + x/      -1 + x        3 + x                       (-1 + x)*(3 + x)                /|
\/  (4 + x)  *|- ---------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------- + --------------------------------------------------------------------------------------------------------------|
              |           3                                                                                                                                                                                              (-1 + x)*(3 + x)                                                                                                                                                                                                                        2                                             2*(-1 + x)*(3 + x)*(4 + x)                                          |
              \  8*(4 + x)                                                                                                                                                                                                                                                                                                                                                                                                             4*(-1 + x)*(3 + x)*(4 + x)                                                                                                                  /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                         2        5                                                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                                                 (-1 + x) *(3 + x)
(−38(x+4)3−2(7x+1)(15(x+3)2+10(x−1)(x+3)+3(x−1)2)+5(7x+1)(5x+3+2x−1)x+3+55(7x+1)(x+3)2+2(7x+1)(5x+3+2x−1)x−1+40(7x+1)(x−1)(x+3)−2(5x+3+2x−1)(10(x−1)2+10(x−1)(x+3)+(x+3)2)(x−1)(x+3)+30(2(x−1)2+4(x−1)(x+3)+(x+3)2)(x−1)(x+3)2−30(10(x−1)2+10(x−1)(x+3)+(x+3)2)(x−1)(x+3)2+10(7x+1)(x−1)2−12(10(x−1)2+10(x−1)(x+3)+(x+3)2)(x−1)2(x+3)(x−1)(x+3)+9((7x+1)(5x+3+2x−1)+5(7x+1)x+3+2(7x+1)x−1−2(10(x−1)2+10(x−1)(x+3)+(x+3)2)(x−1)(x+3))2(x−1)(x+3)(x+4)−9(7x+1)4(x−1)(x+3)(x+4)2)(x+4)3(x−1)2(x+3)5\frac{\left(- \frac{3}{8 \left(x + 4\right)^{3}} - \frac{2 \left(7 x + 1\right) \left(\frac{15}{\left(x + 3\right)^{2}} + \frac{10}{\left(x - 1\right) \left(x + 3\right)} + \frac{3}{\left(x - 1\right)^{2}}\right) + \frac{5 \left(7 x + 1\right) \left(\frac{5}{x + 3} + \frac{2}{x - 1}\right)}{x + 3} + \frac{55 \left(7 x + 1\right)}{\left(x + 3\right)^{2}} + \frac{2 \left(7 x + 1\right) \left(\frac{5}{x + 3} + \frac{2}{x - 1}\right)}{x - 1} + \frac{40 \left(7 x + 1\right)}{\left(x - 1\right) \left(x + 3\right)} - \frac{2 \left(\frac{5}{x + 3} + \frac{2}{x - 1}\right) \left(10 \left(x - 1\right)^{2} + 10 \left(x - 1\right) \left(x + 3\right) + \left(x + 3\right)^{2}\right)}{\left(x - 1\right) \left(x + 3\right)} + \frac{30 \left(2 \left(x - 1\right)^{2} + 4 \left(x - 1\right) \left(x + 3\right) + \left(x + 3\right)^{2}\right)}{\left(x - 1\right) \left(x + 3\right)^{2}} - \frac{30 \left(10 \left(x - 1\right)^{2} + 10 \left(x - 1\right) \left(x + 3\right) + \left(x + 3\right)^{2}\right)}{\left(x - 1\right) \left(x + 3\right)^{2}} + \frac{10 \left(7 x + 1\right)}{\left(x - 1\right)^{2}} - \frac{12 \left(10 \left(x - 1\right)^{2} + 10 \left(x - 1\right) \left(x + 3\right) + \left(x + 3\right)^{2}\right)}{\left(x - 1\right)^{2} \left(x + 3\right)}}{\left(x - 1\right) \left(x + 3\right)} + \frac{9 \left(\left(7 x + 1\right) \left(\frac{5}{x + 3} + \frac{2}{x - 1}\right) + \frac{5 \left(7 x + 1\right)}{x + 3} + \frac{2 \left(7 x + 1\right)}{x - 1} - \frac{2 \left(10 \left(x - 1\right)^{2} + 10 \left(x - 1\right) \left(x + 3\right) + \left(x + 3\right)^{2}\right)}{\left(x - 1\right) \left(x + 3\right)}\right)}{2 \left(x - 1\right) \left(x + 3\right) \left(x + 4\right)} - \frac{9 \left(7 x + 1\right)}{4 \left(x - 1\right) \left(x + 3\right) \left(x + 4\right)^{2}}\right) \sqrt{\left(x + 4\right)^{3}}}{\left(x - 1\right)^{2} \left(x + 3\right)^{5}}
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Gráfico
Derivada de sqrt(((x+4)^3),5)/(((x-1)^2)*(x+3)^5)
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