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Derivada de la función/ y=x^a/ arctg/ y=x^arctg7c

Derivada de y=x^arctg7c

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

Ha introducido [src] 
 atan(7*c)
x
xatan⁡(7c)x^{\operatorname{atan}{\left(7 c \right)}} 
x^atan(7*c)
Solución detallada

  1. Según el principio, aplicamos: xatan⁡(7c)x^{\operatorname{atan}{\left(7 c \right)}} tenemos xatan⁡(7c)atan⁡(7c)x\frac{x^{\operatorname{atan}{\left(7 c \right)}} \operatorname{atan}{\left(7 c \right)}}{x}

  2. Simplificamos:

    xatan⁡(7c)−1atan⁡(7c)x^{\operatorname{atan}{\left(7 c \right)} - 1} \operatorname{atan}{\left(7 c \right)}

Respuesta:

xatan⁡(7c)−1atan⁡(7c)x^{\operatorname{atan}{\left(7 c \right)} - 1} \operatorname{atan}{\left(7 c \right)}

Primera derivada [src] 
 atan(7*c)          
x         *atan(7*c)
--------------------
         x
xatan⁡(7c)atan⁡(7c)x\frac{x^{\operatorname{atan}{\left(7 c \right)}} \operatorname{atan}{\left(7 c \right)}}{x}
Simplificar
Segunda derivada [src] 
 atan(7*c)                           
x         *(-1 + atan(7*c))*atan(7*c)
-------------------------------------
                   2                 
                  x
xatan⁡(7c)(atan⁡(7c)−1)atan⁡(7c)x2\frac{x^{\operatorname{atan}{\left(7 c \right)}} \left(\operatorname{atan}{\left(7 c \right)} - 1\right) \operatorname{atan}{\left(7 c \right)}}{x^{2}}
Simplificar
Tercera derivada [src] 
 atan(7*c) /        2                   \          
x         *\2 + atan (7*c) - 3*atan(7*c)/*atan(7*c)
---------------------------------------------------
                          3                        
                         x
xatan⁡(7c)(atan⁡2(7c)−3atan⁡(7c)+2)atan⁡(7c)x3\frac{x^{\operatorname{atan}{\left(7 c \right)}} \left(\operatorname{atan}^{2}{\left(7 c \right)} - 3 \operatorname{atan}{\left(7 c \right)} + 2\right) \operatorname{atan}{\left(7 c \right)}}{x^{3}}
Simplificar
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