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y=4x^5-thx+x/2sin(x)/x
Derivada de la función/ x+x/2/ y=4x^5/ sin(x)/ y=4x^5-thx+x/2sin(x)/x

Derivada de y=4x^5-thx+x/2sin(x)/x

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

Ha introducido [src] 
                 x       
                 -*sin(x)
   5             2       
4*x  - tanh(x) + --------
                    x
(4x5−tanh⁡(x))+x2sin⁡(x)x\left(4 x^{5} - \tanh{\left(x \right)}\right) + \frac{\frac{x}{2} \sin{\left(x \right)}}{x} 
4*x^5 - tanh(x) + ((x/2)*sin(x))/x
Gráfica
02468-8-6-4-2-1010-10000001000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
                        sin(x)   x*cos(x)         
                        ------ + --------         
         2          4     2         2       sin(x)
-1 + tanh (x) + 20*x  + ----------------- - ------
                                x            2*x
20x4+tanh⁡2(x)−1+xcos⁡(x)2+sin⁡(x)2x−sin⁡(x)2x20 x^{4} + \tanh^{2}{\left(x \right)} - 1 + \frac{\frac{x \cos{\left(x \right)}}{2} + \frac{\sin{\left(x \right)}}{2}}{x} - \frac{\sin{\left(x \right)}}{2 x}
Simplificar
Segunda derivada [src] 
    3   sin(x)     /         2   \           -2*cos(x) + x*sin(x)   cos(x)   x*cos(x) + sin(x)
80*x  + ------ - 2*\-1 + tanh (x)/*tanh(x) - -------------------- - ------ - -----------------
            2                                        2*x             2*x               2      
         2*x                                                                        2*x
80x3−2(tanh⁡2(x)−1)tanh⁡(x)−xsin⁡(x)−2cos⁡(x)2x−cos⁡(x)2x−xcos⁡(x)+sin⁡(x)2x2+sin⁡(x)2x280 x^{3} - 2 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)} - \frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{2 x} - \frac{\cos{\left(x \right)}}{2 x} - \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{2 x^{2}} + \frac{\sin{\left(x \right)}}{2 x^{2}}
Simplificar
Tercera derivada [src] 
                 2                                                                                                                                  
  /         2   \         2   x*cos(x) + sin(x)   -2*cos(x) + x*sin(x)   cos(x)   sin(x)   sin(x)         2    /         2   \   3*sin(x) + x*cos(x)
2*\-1 + tanh (x)/  + 240*x  + ----------------- + -------------------- + ------ + ------ - ------ + 4*tanh (x)*\-1 + tanh (x)/ - -------------------
                                       3                    2               2      2*x        3                                          2*x        
                                      x                    x               x                 x
240x2+2(tanh⁡2(x)−1)2+4(tanh⁡2(x)−1)tanh⁡2(x)−xcos⁡(x)+3sin⁡(x)2x+sin⁡(x)2x+xsin⁡(x)−2cos⁡(x)x2+cos⁡(x)x2+xcos⁡(x)+sin⁡(x)x3−sin⁡(x)x3240 x^{2} + 2 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} + 4 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh^{2}{\left(x \right)} - \frac{x \cos{\left(x \right)} + 3 \sin{\left(x \right)}}{2 x} + \frac{\sin{\left(x \right)}}{2 x} + \frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{3}} - \frac{\sin{\left(x \right)}}{x^{3}}
Simplificar
Gráfico
Derivada de y=4x^5-thx+x/2sin(x)/x
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