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  • Derivada de 7^(3*x-1) Derivada de 7^(3*x-1)
  • Derivada de 6^(x^2-8x+28) Derivada de 6^(x^2-8x+28)
  • Derivada de -5*tan(2*t)-4*cot(4*t) Derivada de -5*tan(2*t)-4*cot(4*t)
  • Derivada de 5(3-2x)^2 Derivada de 5(3-2x)^2

  • Expresiones idénticas

  • x^(e)/((log(cosh(x^e*x))/log(diez)))
  • x en el grado (e) dividir por (( logaritmo de ( coseno de eno hiperbólico de (x en el grado e multiplicar por x)) dividir por logaritmo de (10)))
  • x en el grado (e) dividir por (( logaritmo de ( coseno de eno hiperbólico de (x en el grado e multiplicar por x)) dividir por logaritmo de (diez)))
  • x(e)/((log(cosh(xe*x))/log(10)))
  • xe/logcoshxe*x/log10
  • x^(e)/((log(cosh(x^ex))/log(10)))
  • x(e)/((log(cosh(xex))/log(10)))
  • xe/logcoshxex/log10
  • x^e/logcoshx^ex/log10
  • x^(e) dividir por ((log(cosh(x^e*x)) dividir por log(10)))
Derivada de la función/ x^(e)/((log(cosh(x^e*x))/log(10)))

Derivada de x^(e)/((log(cosh(x^e*x))/log(10)))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
         E       
        x        
-----------------
/   /    / E  \\\
|log\cosh\x *x//|
|---------------|
\    log(10)    /
xe1log⁡(10)log⁡(cosh⁡(xxe))\frac{x^{e}}{\frac{1}{\log{\left(10 \right)}} \log{\left(\cosh{\left(x x^{e} \right)} \right)}} 
x^E/((log(cosh(x^E*x))/log(10)))
Primera derivada [src] 
   E     log(10)                                        
E*x *---------------                                    
        /    / E  \\    E / E      E\             / E  \
     log\cosh\x *x//   x *\x  + E*x /*log(10)*sinh\x *x/
-------------------- - ---------------------------------
         x                    / E  \    2/    / E  \\   
                          cosh\x *x/*log \cosh\x *x//
−xe(xe+exe)log⁡(10)sinh⁡(xxe)log⁡(cosh⁡(xxe))2cosh⁡(xxe)+exelog⁡(10)log⁡(cosh⁡(xxe))x- \frac{x^{e} \left(x^{e} + e x^{e}\right) \log{\left(10 \right)} \sinh{\left(x x^{e} \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}^{2} \cosh{\left(x x^{e} \right)}} + \frac{e x^{e} \frac{\log{\left(10 \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}}}{x}
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Segunda derivada [src] 
   /                         /                E     2/   E\                 /   E\        E     2/   E\         \                               \        
   |               E         |   E           x *sinh \x*x /*(1 + E)   E*sinh\x*x /     2*x *sinh \x*x /*(1 + E) |                               |        
   |              x *(1 + E)*|- x *(1 + E) + ---------------------- - ------------ + ---------------------------|                               |        
   |                         |                        2/   E\               /   E\       2/   E\    /    /   E\\|         E             /   E\  |        
 E |  E*(1 - E)              \                    cosh \x*x /         x*cosh\x*x /   cosh \x*x /*log\cosh\x*x ///    2*E*x *(1 + E)*sinh\x*x /  |        
x *|- --------- + ----------------------------------------------------------------------------------------------- - ----------------------------|*log(10)
   |       2                                                 /    /   E\\                                                 /   E\    /    /   E\\|        
   \      x                                               log\cosh\x*x //                                           x*cosh\x*x /*log\cosh\x*x ///        
---------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                        /    /   E\\                                                                     
                                                                     log\cosh\x*x //
xe(xe(1+e)(xe(1+e)sinh⁡2(xxe)cosh⁡2(xxe)−xe(1+e)+2xe(1+e)sinh⁡2(xxe)log⁡(cosh⁡(xxe))cosh⁡2(xxe)−esinh⁡(xxe)xcosh⁡(xxe))log⁡(cosh⁡(xxe))−2exe(1+e)sinh⁡(xxe)xlog⁡(cosh⁡(xxe))cosh⁡(xxe)−e(1−e)x2)log⁡(10)log⁡(cosh⁡(xxe))\frac{x^{e} \left(\frac{x^{e} \left(1 + e\right) \left(\frac{x^{e} \left(1 + e\right) \sinh^{2}{\left(x x^{e} \right)}}{\cosh^{2}{\left(x x^{e} \right)}} - x^{e} \left(1 + e\right) + \frac{2 x^{e} \left(1 + e\right) \sinh^{2}{\left(x x^{e} \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh^{2}{\left(x x^{e} \right)}} - \frac{e \sinh{\left(x x^{e} \right)}}{x \cosh{\left(x x^{e} \right)}}\right)}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}} - \frac{2 e x^{e} \left(1 + e\right) \sinh{\left(x x^{e} \right)}}{x \log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh{\left(x x^{e} \right)}} - \frac{e \left(1 - e\right)}{x^{2}}\right) \log{\left(10 \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}}
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Tercera derivada [src] 
   /                      /       E        2      2*E        3     3/   E\      2*E        3     /   E\     /     2\     /   E\      2*E        3     3/   E\      2*E        3     3/   E\       2*E        3     /   E\        E        2     2/   E\         E        2     2/   E\ \                  /                E     2/   E\                 /   E\        E     2/   E\         \                                    \        
   |                    E |  3*E*x *(1 + E)    2*x   *(1 + E) *sinh \x*x /   2*x   *(1 + E) *sinh\x*x /   E*\1 - e /*sinh\x*x /   6*x   *(1 + E) *sinh \x*x /   6*x   *(1 + E) *sinh \x*x /    6*x   *(1 + E) *sinh\x*x /   3*E*x *(1 + E) *sinh \x*x /    6*E*x *(1 + E) *sinh \x*x / |        E         |   E           x *sinh \x*x /*(1 + E)   E*sinh\x*x /     2*x *sinh \x*x /*(1 + E) |                                    |        
   |                   x *|- --------------- - --------------------------- + -------------------------- + --------------------- - --------------------------- - ---------------------------- + -------------------------- + --------------------------- + -----------------------------|   3*E*x *(1 + E)*|- x *(1 + E) + ---------------------- - ------------ + ---------------------------|                                    |        
   |  /           2\      |         x                      3/   E\                       /   E\                2     /   E\           3/   E\    /    /   E\\       3/   E\    2/    /   E\\       /   E\    /    /   E\\                2/   E\                2/   E\    /    /   E\\|                  |                        2/   E\               /   E\       2/   E\    /    /   E\\|        E                     /   E\|        
 E |E*\2 - 3*E + e /      \                            cosh \x*x /                   cosh\x*x /               x *cosh\x*x /       cosh \x*x /*log\cosh\x*x //   cosh \x*x /*log \cosh\x*x //   cosh\x*x /*log\cosh\x*x //          x*cosh \x*x /          x*cosh \x*x /*log\cosh\x*x ///                  \                    cosh \x*x /         x*cosh\x*x /   cosh \x*x /*log\cosh\x*x ///   3*E*x *(1 + E)*(1 - E)*sinh\x*x /|        
x *|---------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------- + ---------------------------------|*log(10)
   |        3                                                                                                                                      /    /   E\\                                                                                                                                                                          /    /   E\\                                               2     /   E\    /    /   E\\  |        
   \       x                                                                                                                                    log\cosh\x*x //                                                                                                                                                                     x*log\cosh\x*x //                                              x *cosh\x*x /*log\cosh\x*x //  /        
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                 /    /   E\\                                                                                                                                                                                                              
                                                                                                                                                                                                              log\cosh\x*x //
xe(xe(−2x2e(1+e)3sinh⁡3(xxe)cosh⁡3(xxe)+2x2e(1+e)3sinh⁡(xxe)cosh⁡(xxe)−6x2e(1+e)3sinh⁡3(xxe)log⁡(cosh⁡(xxe))cosh⁡3(xxe)+6x2e(1+e)3sinh⁡(xxe)log⁡(cosh⁡(xxe))cosh⁡(xxe)−6x2e(1+e)3sinh⁡3(xxe)log⁡(cosh⁡(xxe))2cosh⁡3(xxe)+3exe(1+e)2sinh⁡2(xxe)xcosh⁡2(xxe)−3exe(1+e)2x+6exe(1+e)2sinh⁡2(xxe)xlog⁡(cosh⁡(xxe))cosh⁡2(xxe)+e(1−e2)sinh⁡(xxe)x2cosh⁡(xxe))log⁡(cosh⁡(xxe))+3exe(1+e)(xe(1+e)sinh⁡2(xxe)cosh⁡2(xxe)−xe(1+e)+2xe(1+e)sinh⁡2(xxe)log⁡(cosh⁡(xxe))cosh⁡2(xxe)−esinh⁡(xxe)xcosh⁡(xxe))xlog⁡(cosh⁡(xxe))+3exe(1−e)(1+e)sinh⁡(xxe)x2log⁡(cosh⁡(xxe))cosh⁡(xxe)+e(−3e+2+e2)x3)log⁡(10)log⁡(cosh⁡(xxe))\frac{x^{e} \left(\frac{x^{e} \left(- \frac{2 x^{2 e} \left(1 + e\right)^{3} \sinh^{3}{\left(x x^{e} \right)}}{\cosh^{3}{\left(x x^{e} \right)}} + \frac{2 x^{2 e} \left(1 + e\right)^{3} \sinh{\left(x x^{e} \right)}}{\cosh{\left(x x^{e} \right)}} - \frac{6 x^{2 e} \left(1 + e\right)^{3} \sinh^{3}{\left(x x^{e} \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh^{3}{\left(x x^{e} \right)}} + \frac{6 x^{2 e} \left(1 + e\right)^{3} \sinh{\left(x x^{e} \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh{\left(x x^{e} \right)}} - \frac{6 x^{2 e} \left(1 + e\right)^{3} \sinh^{3}{\left(x x^{e} \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}^{2} \cosh^{3}{\left(x x^{e} \right)}} + \frac{3 e x^{e} \left(1 + e\right)^{2} \sinh^{2}{\left(x x^{e} \right)}}{x \cosh^{2}{\left(x x^{e} \right)}} - \frac{3 e x^{e} \left(1 + e\right)^{2}}{x} + \frac{6 e x^{e} \left(1 + e\right)^{2} \sinh^{2}{\left(x x^{e} \right)}}{x \log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh^{2}{\left(x x^{e} \right)}} + \frac{e \left(1 - e^{2}\right) \sinh{\left(x x^{e} \right)}}{x^{2} \cosh{\left(x x^{e} \right)}}\right)}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}} + \frac{3 e x^{e} \left(1 + e\right) \left(\frac{x^{e} \left(1 + e\right) \sinh^{2}{\left(x x^{e} \right)}}{\cosh^{2}{\left(x x^{e} \right)}} - x^{e} \left(1 + e\right) + \frac{2 x^{e} \left(1 + e\right) \sinh^{2}{\left(x x^{e} \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh^{2}{\left(x x^{e} \right)}} - \frac{e \sinh{\left(x x^{e} \right)}}{x \cosh{\left(x x^{e} \right)}}\right)}{x \log{\left(\cosh{\left(x x^{e} \right)} \right)}} + \frac{3 e x^{e} \left(1 - e\right) \left(1 + e\right) \sinh{\left(x x^{e} \right)}}{x^{2} \log{\left(\cosh{\left(x x^{e} \right)} \right)} \cosh{\left(x x^{e} \right)}} + \frac{e \left(- 3 e + 2 + e^{2}\right)}{x^{3}}\right) \log{\left(10 \right)}}{\log{\left(\cosh{\left(x x^{e} \right)} \right)}}
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