Sr Examen

Derivada de y=sin(e)^x-arctg(2x)

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

Gráfico:

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Solución

Ha introducido [src]
   x               
sin (E) - atan(2*x)
$$\sin^{x}{\left(e \right)} - \operatorname{atan}{\left(2 x \right)}$$
sin(E)^x - atan(2*x)
Gráfica
Primera derivada [src]
     2          x               
- -------- + sin (E)*log(sin(E))
         2                      
  1 + 4*x                       
$$\log{\left(\sin{\left(e \right)} \right)} \sin^{x}{\left(e \right)} - \frac{2}{4 x^{2} + 1}$$
Segunda derivada [src]
   2            x          16*x   
log (sin(E))*sin (E) + -----------
                                 2
                       /       2\ 
                       \1 + 4*x / 
$$\frac{16 x}{\left(4 x^{2} + 1\right)^{2}} + \log{\left(\sin{\left(e \right)} \right)}^{2} \sin^{x}{\left(e \right)}$$
Tercera derivada [src]
                                             2  
     16          3            x         256*x   
----------- + log (sin(E))*sin (E) - -----------
          2                                    3
/       2\                           /       2\ 
\1 + 4*x /                           \1 + 4*x / 
$$- \frac{256 x^{2}}{\left(4 x^{2} + 1\right)^{3}} + \log{\left(\sin{\left(e \right)} \right)}^{3} \sin^{x}{\left(e \right)} + \frac{16}{\left(4 x^{2} + 1\right)^{2}}$$
Gráfico
Derivada de y=sin(e)^x-arctg(2x)