Sr Examen

Derivada de atan(e)^x

Función f() - derivada -er orden en el punto
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Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
    x   
atan (E)
atanx(e)\operatorname{atan}^{x}{\left(e \right)}
atan(E)^x
Solución detallada
  1. ddxatanx(e)=log(atan(e))atanx(e)\frac{d}{d x} \operatorname{atan}^{x}{\left(e \right)} = \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{x}{\left(e \right)}


Respuesta:

log(atan(e))atanx(e)\log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{x}{\left(e \right)}

Gráfica
02468-8-6-4-2-1010010
Primera derivada [src]
    x                
atan (E)*log(atan(E))
log(atan(e))atanx(e)\log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{x}{\left(e \right)}
Segunda derivada [src]
    x       2         
atan (E)*log (atan(E))
log(atan(e))2atanx(e)\log{\left(\operatorname{atan}{\left(e \right)} \right)}^{2} \operatorname{atan}^{x}{\left(e \right)}
Tercera derivada [src]
    x       3         
atan (E)*log (atan(E))
log(atan(e))3atanx(e)\log{\left(\operatorname{atan}{\left(e \right)} \right)}^{3} \operatorname{atan}^{x}{\left(e \right)}
Gráfico
Derivada de atan(e)^x