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Derivada de la función/ (x-1)/ xsqrt/ е^xsqrt^7(x^6)/(x-1)^5

Derivada de е^xsqrt^7(x^6)/(x-1)^5

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
          7
      ____ 
 x   /  6  
E *\/  x   
-----------
         5 
  (x - 1)
ex(x6)7(x−1)5\frac{e^{x} \left(\sqrt{x^{6}}\right)^{7}}{\left(x - 1\right)^{5}} 
(E^x*(sqrt(x^6))^7)/(x - 1)^5
Primera derivada [src] 
 20      x       19      x      20      x
x  *|x|*e  + 21*x  *|x|*e    5*x  *|x|*e 
-------------------------- - ------------
                5                     6  
         (x - 1)               (x - 1)
−5x20∣x∣ex(x−1)6+21x19ex∣x∣+x20∣x∣ex(x−1)5- \frac{5 x^{20} \left|{x}\right| e^{x}}{\left(x - 1\right)^{6}} + \frac{21 x^{19} e^{x} \left|{x}\right| + x^{20} \left|{x}\right| e^{x}}{\left(x - 1\right)^{5}}
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Segunda derivada [src] 
    /                                                 2                        \   
 18 |           2                                 30*x *|x|   10*x*(21 + x)*|x||  x
x  *|399*|x| + x *|x| + 21*x*sign(x) + 42*x*|x| + --------- - -----------------|*e 
    |                                                     2         -1 + x     |   
    \                                             (-1 + x)                     /   
-----------------------------------------------------------------------------------
                                             5                                     
                                     (-1 + x)
x18(x2∣x∣+30x2∣x∣(x−1)2+42x∣x∣+21xsign⁡(x)−10x(x+21)∣x∣x−1+399∣x∣)ex(x−1)5\frac{x^{18} \left(x^{2} \left|{x}\right| + \frac{30 x^{2} \left|{x}\right|}{\left(x - 1\right)^{2}} + 42 x \left|{x}\right| + 21 x \operatorname{sign}{\left(x \right)} - \frac{10 x \left(x + 21\right) \left|{x}\right|}{x - 1} + 399 \left|{x}\right|\right) e^{x}}{\left(x - 1\right)^{5}}
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Tercera derivada [src] 
    /                                                                                                       3            /           2                              \       2             \   
 17 |            3           2                                                 2                       210*x *|x|   15*x*\399*|x| + x *|x| + 21*x*sign(x) + 42*x*|x|/   90*x *(21 + x)*|x||  x
x  *|7182*|x| + x *|x| + 42*x *DiracDelta(x) + 63*x*(19*|x| + x*sign(x)) + 63*x *|x| + 798*x*sign(x) - ---------- - ------------------------------------------------- + ------------------|*e 
    |                                                                                                          3                          -1 + x                                    2     |   
    \                                                                                                  (-1 + x)                                                             (-1 + x)      /   
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                  5                                                                                           
                                                                                          (-1 + x)
x17(x3∣x∣−210x3∣x∣(x−1)3+63x2∣x∣+42x2δ(x)+90x2(x+21)∣x∣(x−1)2+63x(xsign⁡(x)+19∣x∣)+798xsign⁡(x)−15x(x2∣x∣+42x∣x∣+21xsign⁡(x)+399∣x∣)x−1+7182∣x∣)ex(x−1)5\frac{x^{17} \left(x^{3} \left|{x}\right| - \frac{210 x^{3} \left|{x}\right|}{\left(x - 1\right)^{3}} + 63 x^{2} \left|{x}\right| + 42 x^{2} \delta\left(x\right) + \frac{90 x^{2} \left(x + 21\right) \left|{x}\right|}{\left(x - 1\right)^{2}} + 63 x \left(x \operatorname{sign}{\left(x \right)} + 19 \left|{x}\right|\right) + 798 x \operatorname{sign}{\left(x \right)} - \frac{15 x \left(x^{2} \left|{x}\right| + 42 x \left|{x}\right| + 21 x \operatorname{sign}{\left(x \right)} + 399 \left|{x}\right|\right)}{x - 1} + 7182 \left|{x}\right|\right) e^{x}}{\left(x - 1\right)^{5}}
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