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x*tg2^x
Derivada de la función/ x*tg2/ x*tg2^x

Derivada de x*tg2^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   
x*tan (2)
xtan⁡x(2)x \tan^{x}{\left(2 \right)} 
x*tan(2)^x
Solución detallada

  1. Se aplica la regla de la derivada de una multiplicación:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=xf{\left(x \right)} = x; calculamos ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Según el principio, aplicamos: xx tenemos 11

    g(x)=tan⁡x(2)g{\left(x \right)} = \tan^{x}{\left(2 \right)}; calculamos ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. ddxtan⁡x(2)=(log⁡(−tan⁡(2))+iπ)tan⁡x(2)\frac{d}{d x} \tan^{x}{\left(2 \right)} = \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \tan^{x}{\left(2 \right)}

    Como resultado de: x(log⁡(−tan⁡(2))+iπ)tan⁡x(2)+tan⁡x(2)x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \tan^{x}{\left(2 \right)} + \tan^{x}{\left(2 \right)}

  2. Simplificamos:

    (x(log⁡(−tan⁡(2))+iπ)+1)tan⁡x(2)\left(x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) + 1\right) \tan^{x}{\left(2 \right)}

Respuesta:

(x(log⁡(−tan⁡(2))+iπ)+1)tan⁡x(2)\left(x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) + 1\right) \tan^{x}{\left(2 \right)}

Gráfica
02468-8-6-4-2-101050000-25000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   x           x                         
tan (2) + x*tan (2)*(pi*I + log(-tan(2)))
x(log⁡(−tan⁡(2))+iπ)tan⁡x(2)+tan⁡x(2)x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \tan^{x}{\left(2 \right)} + \tan^{x}{\left(2 \right)}
Simplificar
Segunda derivada [src] 
   x                                                       
tan (2)*(2 + x*(pi*I + log(-tan(2))))*(pi*I + log(-tan(2)))
(x(log⁡(−tan⁡(2))+iπ)+2)(log⁡(−tan⁡(2))+iπ)tan⁡x(2)\left(x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) + 2\right) \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \tan^{x}{\left(2 \right)}
Simplificar
Tercera derivada [src] 
                     2    x                                 
(pi*I + log(-tan(2))) *tan (2)*(3 + x*(pi*I + log(-tan(2))))
(x(log⁡(−tan⁡(2))+iπ)+3)(log⁡(−tan⁡(2))+iπ)2tan⁡x(2)\left(x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) + 3\right) \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \tan^{x}{\left(2 \right)}
Simplificar
Gráfico
Derivada de x*tg2^x
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