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Derivada de la función/ sqrt(3x)/ x*exatan(sqrt(3x))p(-x)

Derivada de x*exatan(sqrt(3x))p(-x)

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

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Solución

Ha introducido [src] 
   x     /  _____\       
x*E *atan\\/ 3*x /*p*(-x)
−xpexxatan⁡(3x)- x p e^{x} x \operatorname{atan}{\left(\sqrt{3 x} \right)} 
(((x*E^x)*atan(sqrt(3*x)))*p)*(-x)
Primera derivada [src] 
      /                              ___   ___  x\                       
      |/ x      x\     /  _____\   \/ 3 *\/ x *e |           /  _____\  x
- p*x*|\E  + x*e /*atan\\/ 3*x / + --------------| - p*x*atan\\/ 3*x /*e 
      \                             2*(1 + 3*x)  /
−px(3xex2(3x+1)+(ex+xex)atan⁡(3x))−pxexatan⁡(3x)- p x \left(\frac{\sqrt{3} \sqrt{x} e^{x}}{2 \left(3 x + 1\right)} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(\sqrt{3 x} \right)}\right) - p x e^{x} \operatorname{atan}{\left(\sqrt{3 x} \right)}
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Segunda derivada [src] 
   /                            /                            ___   ___ /1      6   \                  \              \   
   |                            |                          \/ 3 *\/ x *|- + -------|       ___        |              |   
   |                            |              /  _____\               \x   1 + 3*x/   4*\/ 3 *(1 + x)|              |   
   |                          x*|4*(2 + x)*atan\\/ 3*x / - ------------------------- + ---------------|              |   
   |                            |                                   1 + 3*x              ___          |     ___   ___|   
   |              /  _____\     \                                                      \/ x *(1 + 3*x)/   \/ 3 *\/ x |  x
-p*|2*(1 + x)*atan\\/ 3*x / + ------------------------------------------------------------------------- + -----------|*e 
   \                                                              4                                         1 + 3*x  /
−p(3x3x+1+x(−3x(63x+1+1x)3x+1+4(x+2)atan⁡(3x)+43(x+1)x(3x+1))4+2(x+1)atan⁡(3x))ex- p \left(\frac{\sqrt{3} \sqrt{x}}{3 x + 1} + \frac{x \left(- \frac{\sqrt{3} \sqrt{x} \left(\frac{6}{3 x + 1} + \frac{1}{x}\right)}{3 x + 1} + 4 \left(x + 2\right) \operatorname{atan}{\left(\sqrt{3 x} \right)} + \frac{4 \sqrt{3} \left(x + 1\right)}{\sqrt{x} \left(3 x + 1\right)}\right)}{4} + 2 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{3 x} \right)}\right) e^{x}
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Tercera derivada [src] 
   /                            /                              ___   ___ /1        24            4     \                                                   \                                                \   
   |                            |                          3*\/ 3 *\/ x *|-- + ---------- + -----------|                          ___         /1      6   \|                                                |   
   |                            |                                        | 2            2   x*(1 + 3*x)|        ___           6*\/ 3 *(1 + x)*|- + -------||                                                |   
   |                            |              /  _____\                 \x    (1 + 3*x)               /   12*\/ 3 *(2 + x)                   \x   1 + 3*x/|                                                |   
   |                          x*|8*(3 + x)*atan\\/ 3*x / + --------------------------------------------- + ---------------- - -----------------------------|                         ___   ___ /1      6   \|   
   |                            |                                             1 + 3*x                        ___                       ___                 |       ___           3*\/ 3 *\/ x *|- + -------||   
   |              /  _____\     \                                                                          \/ x *(1 + 3*x)           \/ x *(1 + 3*x)       /   3*\/ 3 *(1 + x)                 \x   1 + 3*x/|  x
-p*|3*(2 + x)*atan\\/ 3*x / + ------------------------------------------------------------------------------------------------------------------------------ + --------------- - ---------------------------|*e 
   |                                                                                        8                                                                    ___                     4*(1 + 3*x)        |   
   \                                                                                                                                                           \/ x *(1 + 3*x)                              /
−p(−33x(63x+1+1x)4(3x+1)+x(33x(24(3x+1)2+4x(3x+1)+1x2)3x+1+8(x+3)atan⁡(3x)−63(x+1)(63x+1+1x)x(3x+1)+123(x+2)x(3x+1))8+3(x+2)atan⁡(3x)+33(x+1)x(3x+1))ex- p \left(- \frac{3 \sqrt{3} \sqrt{x} \left(\frac{6}{3 x + 1} + \frac{1}{x}\right)}{4 \left(3 x + 1\right)} + \frac{x \left(\frac{3 \sqrt{3} \sqrt{x} \left(\frac{24}{\left(3 x + 1\right)^{2}} + \frac{4}{x \left(3 x + 1\right)} + \frac{1}{x^{2}}\right)}{3 x + 1} + 8 \left(x + 3\right) \operatorname{atan}{\left(\sqrt{3 x} \right)} - \frac{6 \sqrt{3} \left(x + 1\right) \left(\frac{6}{3 x + 1} + \frac{1}{x}\right)}{\sqrt{x} \left(3 x + 1\right)} + \frac{12 \sqrt{3} \left(x + 2\right)}{\sqrt{x} \left(3 x + 1\right)}\right)}{8} + 3 \left(x + 2\right) \operatorname{atan}{\left(\sqrt{3 x} \right)} + \frac{3 \sqrt{3} \left(x + 1\right)}{\sqrt{x} \left(3 x + 1\right)}\right) e^{x}
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