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y=arctg^2e^x
Derivada de la función/ ctg^2/ arctg/ y=arctg^2e^x

Derivada de y=arctg^2e^x

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

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Definida a trozos:

Solución

Ha introducido [src] 
         / x\
         \2 /
(atan(E))
atan⁡2x(e)\operatorname{atan}^{2^{x}}{\left(e \right)} 
atan(E)^(2^x)
Solución detallada

  1. Sustituimos u=2xu = 2^{x}.

  2. dduatan⁡u(e)=log⁡(atan⁡(e))atan⁡u(e)\frac{d}{d u} \operatorname{atan}^{u}{\left(e \right)} = \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{u}{\left(e \right)}

  3. Luego se aplica una cadena de reglas. Multiplicamos por ddx2x\frac{d}{d x} 2^{x}:

    1. ddx2x=2xlog⁡(2)\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}

    Como resultado de la secuencia de reglas:

    2xlog⁡(2)log⁡(atan⁡(e))atan⁡2x(e)2^{x} \log{\left(2 \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{2^{x}}{\left(e \right)}

Respuesta:

2xlog⁡(2)log⁡(atan⁡(e))atan⁡2x(e)2^{x} \log{\left(2 \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{2^{x}}{\left(e \right)}

Gráfica
02468-8-6-4-2-101001e90
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
            / x\                    
 x          \2 /                    
2 *(atan(E))    *log(2)*log(atan(E))
2xlog⁡(2)log⁡(atan⁡(e))atan⁡2x(e)2^{x} \log{\left(2 \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{2^{x}}{\left(e \right)}
Simplificar
Segunda derivada [src] 
            / x\                                           
 x          \2 /    2    /     x             \             
2 *(atan(E))    *log (2)*\1 + 2 *log(atan(E))/*log(atan(E))
2x(2xlog⁡(atan⁡(e))+1)log⁡(2)2log⁡(atan⁡(e))atan⁡2x(e)2^{x} \left(2^{x} \log{\left(\operatorname{atan}{\left(e \right)} \right)} + 1\right) \log{\left(2 \right)}^{2} \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{2^{x}}{\left(e \right)}
Simplificar
Tercera derivada [src] 
            / x\                                                                  
 x          \2 /    3    /     2*x    2               x             \             
2 *(atan(E))    *log (2)*\1 + 2   *log (atan(E)) + 3*2 *log(atan(E))/*log(atan(E))
2x(22xlog⁡(atan⁡(e))2+3⋅2xlog⁡(atan⁡(e))+1)log⁡(2)3log⁡(atan⁡(e))atan⁡2x(e)2^{x} \left(2^{2 x} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{2} + 3 \cdot 2^{x} \log{\left(\operatorname{atan}{\left(e \right)} \right)} + 1\right) \log{\left(2 \right)}^{3} \log{\left(\operatorname{atan}{\left(e \right)} \right)} \operatorname{atan}^{2^{x}}{\left(e \right)}
Simplificar
Gráfico
Derivada de y=arctg^2e^x
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