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Derivada de la función/ y=3^sqrt(x^3+x)/sqrt((x-1)^2)

Derivada de y=3^sqrt(x^3+x)/sqrt((x-1)^2)

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

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Solución

Ha introducido [src] 
     ________
    /  3     
  \/  x  + x 
 3           
-------------
   __________
  /        2 
\/  (x - 1)
3x3+x(x−1)2\frac{3^{\sqrt{x^{3} + x}}}{\sqrt{\left(x - 1\right)^{2}}} 
3^(sqrt(x^3 + x))/sqrt((x - 1)^2)
Primera derivada [src] 
                              ________                  
      ________               /  3      /       2\       
     /  3                  \/  x  + x  |1   3*x |       
   \/  x  + x             3           *|- + ----|*log(3)
  3           *(-1 + x)                \2    2  /       
- --------------------- + ------------------------------
            2                     ________              
     (x - 1) *|x - 1|            /  3                   
                               \/  x  + x *|x - 1|
−3x3+x(x−1)(x−1)2∣x−1∣+3x3+x(3x22+12)log⁡(3)x3+x∣x−1∣- \frac{3^{\sqrt{x^{3} + x}} \left(x - 1\right)}{\left(x - 1\right)^{2} \left|{x - 1}\right|} + \frac{3^{\sqrt{x^{3} + x}} \left(\frac{3 x^{2}}{2} + \frac{1}{2}\right) \log{\left(3 \right)}}{\sqrt{x^{3} + x} \left|{x - 1}\right|}
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Segunda derivada [src] 
                   /                          /                          2                2       \                                             \
                   |                          |       ___      /       2\       /       2\        |                                             |
                   |                          |  12*\/ x       \1 + 3*x /       \1 + 3*x / *log(3)|                                             |
                   |                          |----------- - ---------------- + ------------------|*log(3)                                      |
          ________ |   1       sign(-1 + x)   |   ________                3/2         /     2\    |                                             |
   ___   /      2  |-------- + ------------   |  /      2     3/2 /     2\          x*\1 + x /    |                   /       2\                |
 \/ x *\/  1 + x   ||-1 + x|      -1 + x      \\/  1 + x     x   *\1 + x /                        /                   \1 + 3*x /*log(3)         |
3                 *|----------------------- + ------------------------------------------------------------ - -----------------------------------|
                   |               2                                   4*|-1 + x|                                     ________                  |
                   |       (-1 + x)                                                                            ___   /      2                   |
                   \                                                                                         \/ x *\/  1 + x  *(-1 + x)*|-1 + x|/
3xx2+1((12xx2+1+(3x2+1)2log⁡(3)x(x2+1)−(3x2+1)2x32(x2+1)32)log⁡(3)4∣x−1∣+1∣x−1∣+sign⁡(x−1)x−1(x−1)2−(3x2+1)log⁡(3)x(x−1)x2+1∣x−1∣)3^{\sqrt{x} \sqrt{x^{2} + 1}} \left(\frac{\left(\frac{12 \sqrt{x}}{\sqrt{x^{2} + 1}} + \frac{\left(3 x^{2} + 1\right)^{2} \log{\left(3 \right)}}{x \left(x^{2} + 1\right)} - \frac{\left(3 x^{2} + 1\right)^{2}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(3 \right)}}{4 \left|{x - 1}\right|} + \frac{\frac{1}{\left|{x - 1}\right|} + \frac{\operatorname{sign}{\left(x - 1 \right)}}{x - 1}}{\left(x - 1\right)^{2}} - \frac{\left(3 x^{2} + 1\right) \log{\left(3 \right)}}{\sqrt{x} \left(x - 1\right) \sqrt{x^{2} + 1} \left|{x - 1}\right|}\right)
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Tercera derivada [src] 
                   /                                                       /                                                     3                                      3                       3       \            /                          2                2       \                                                       \
                   |                                                       |                         /       2\        /       2\         /       2\          /       2\     2        /       2\        |            |       ___      /       2\       /       2\        |                                                       |
                   |                                                       |        24            36*\1 + 3*x /      3*\1 + 3*x /      36*\1 + 3*x /*log(3)   \1 + 3*x / *log (3)   3*\1 + 3*x / *log(3)|            |  12*\/ x       \1 + 3*x /       \1 + 3*x / *log(3)|                                                       |
                   |                                                       |----------------- - ----------------- + ---------------- + -------------------- + ------------------- - --------------------|*log(3)   3*|----------- - ---------------- + ------------------|*log(3)                                                |
          ________ |    /   1                            2*sign(-1 + x)\   |         ________                 3/2                5/2               2                         3/2                   2    |            |   ________                3/2         /     2\    |            /       2\ /   1       sign(-1 + x)\       |
   ___   /      2  |  2*|-------- - DiracDelta(-1 + x) + --------------|   |  ___   /      2      ___ /     2\       5/2 /     2\             1 + x              3/2 /     2\            2 /     2\     |            |  /      2     3/2 /     2\          x*\1 + x /    |          3*\1 + 3*x /*|-------- + ------------|*log(3)|
 \/ x *\/  1 + x   |    \|-1 + x|                            -1 + x    /   \\/ x *\/  1 + x     \/ x *\1 + x /      x   *\1 + x /                               x   *\1 + x /           x *\1 + x /     /            \\/  1 + x     x   *\1 + x /                        /                       \|-1 + x|      -1 + x   /       |
3                 *|- -------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------- + ---------------------------------------------|
                   |                              3                                                                                      8*|-1 + x|                                                                                     4*(-1 + x)*|-1 + x|                                            ________                  |
                   |                      (-1 + x)                                                                                                                                                                                                                                              ___   /      2          2        |
                   \                                                                                                                                                                                                                                                                        2*\/ x *\/  1 + x  *(-1 + x)         /
3xx2+1((36(3x2+1)log⁡(3)x2+1−3(3x2+1)3log⁡(3)x2(x2+1)2+24xx2+1−36(3x2+1)x(x2+1)32+(3x2+1)3log⁡(3)2x32(x2+1)32+3(3x2+1)3x52(x2+1)52)log⁡(3)8∣x−1∣−3(12xx2+1+(3x2+1)2log⁡(3)x(x2+1)−(3x2+1)2x32(x2+1)32)log⁡(3)4(x−1)∣x−1∣−2(−δ(x−1)+1∣x−1∣+2sign⁡(x−1)x−1)(x−1)3+3(3x2+1)(1∣x−1∣+sign⁡(x−1)x−1)log⁡(3)2x(x−1)2x2+1)3^{\sqrt{x} \sqrt{x^{2} + 1}} \left(\frac{\left(\frac{36 \left(3 x^{2} + 1\right) \log{\left(3 \right)}}{x^{2} + 1} - \frac{3 \left(3 x^{2} + 1\right)^{3} \log{\left(3 \right)}}{x^{2} \left(x^{2} + 1\right)^{2}} + \frac{24}{\sqrt{x} \sqrt{x^{2} + 1}} - \frac{36 \left(3 x^{2} + 1\right)}{\sqrt{x} \left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{\left(3 x^{2} + 1\right)^{3} \log{\left(3 \right)}^{2}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3 \left(3 x^{2} + 1\right)^{3}}{x^{\frac{5}{2}} \left(x^{2} + 1\right)^{\frac{5}{2}}}\right) \log{\left(3 \right)}}{8 \left|{x - 1}\right|} - \frac{3 \left(\frac{12 \sqrt{x}}{\sqrt{x^{2} + 1}} + \frac{\left(3 x^{2} + 1\right)^{2} \log{\left(3 \right)}}{x \left(x^{2} + 1\right)} - \frac{\left(3 x^{2} + 1\right)^{2}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(3 \right)}}{4 \left(x - 1\right) \left|{x - 1}\right|} - \frac{2 \left(- \delta\left(x - 1\right) + \frac{1}{\left|{x - 1}\right|} + \frac{2 \operatorname{sign}{\left(x - 1 \right)}}{x - 1}\right)}{\left(x - 1\right)^{3}} + \frac{3 \left(3 x^{2} + 1\right) \left(\frac{1}{\left|{x - 1}\right|} + \frac{\operatorname{sign}{\left(x - 1 \right)}}{x - 1}\right) \log{\left(3 \right)}}{2 \sqrt{x} \left(x - 1\right)^{2} \sqrt{x^{2} + 1}}\right)
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