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(2*x+3)^tan(x)
Derivada de la función/ 2*x+3/ tan(x)/ (2*x+3)^tan(x)

Derivada de (2*x+3)^tan(x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
         tan(x)
(2*x + 3)
(2x+3)tan⁡(x)\left(2 x + 3\right)^{\tan{\left(x \right)}} 
(2*x + 3)^tan(x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(tan⁡(x))+1)tan⁡tan⁡(x)(x)\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(tan⁡(x))+1)tan⁡tan⁡(x)(x)\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-1010-2500000000000000000025000000000000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         tan(x) //       2   \                2*tan(x)\
(2*x + 3)      *|\1 + tan (x)/*log(2*x + 3) + --------|
                \                             2*x + 3 /
(2x+3)tan⁡(x)((tan⁡2(x)+1)log⁡(2x+3)+2tan⁡(x)2x+3)\left(2 x + 3\right)^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} + \frac{2 \tan{\left(x \right)}}{2 x + 3}\right)
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Segunda derivada [src] 
                /                                       2                  /       2   \                                      \
         tan(x) |//       2   \                2*tan(x)\     4*tan(x)    4*\1 + tan (x)/     /       2   \                    |
(3 + 2*x)      *||\1 + tan (x)/*log(3 + 2*x) + --------|  - ---------- + --------------- + 2*\1 + tan (x)/*log(3 + 2*x)*tan(x)|
                |\                             3 + 2*x /             2       3 + 2*x                                          |
                \                                           (3 + 2*x)                                                         /
(2x+3)tan⁡(x)(((tan⁡2(x)+1)log⁡(2x+3)+2tan⁡(x)2x+3)2+2(tan⁡2(x)+1)log⁡(2x+3)tan⁡(x)+4(tan⁡2(x)+1)2x+3−4tan⁡(x)(2x+3)2)\left(2 x + 3\right)^{\tan{\left(x \right)}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} + \frac{2 \tan{\left(x \right)}}{2 x + 3}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} \tan{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{2 x + 3} - \frac{4 \tan{\left(x \right)}}{\left(2 x + 3\right)^{2}}\right)
Simplificar
Tercera derivada [src] 
                /                                       3      /       2   \                  2                                                          /                 /       2   \                                    \                                                          /       2   \       \
         tan(x) |//       2   \                2*tan(x)\    12*\1 + tan (x)/     /       2   \                   //       2   \                2*tan(x)\ |   2*tan(x)    2*\1 + tan (x)/   /       2   \                    |   16*tan(x)         2    /       2   \                12*\1 + tan (x)/*tan(x)|
(3 + 2*x)      *||\1 + tan (x)/*log(3 + 2*x) + --------|  - ---------------- + 2*\1 + tan (x)/ *log(3 + 2*x) + 6*|\1 + tan (x)/*log(3 + 2*x) + --------|*|- ---------- + --------------- + \1 + tan (x)/*log(3 + 2*x)*tan(x)| + ---------- + 4*tan (x)*\1 + tan (x)/*log(3 + 2*x) + -----------------------|
                |\                             3 + 2*x /                2                                        \                             3 + 2*x / |           2       3 + 2*x                                        |            3                                                  3 + 2*x        |
                \                                              (3 + 2*x)                                                                                 \  (3 + 2*x)                                                       /   (3 + 2*x)                                                                  /
(2x+3)tan⁡(x)(((tan⁡2(x)+1)log⁡(2x+3)+2tan⁡(x)2x+3)3+6((tan⁡2(x)+1)log⁡(2x+3)+2tan⁡(x)2x+3)((tan⁡2(x)+1)log⁡(2x+3)tan⁡(x)+2(tan⁡2(x)+1)2x+3−2tan⁡(x)(2x+3)2)+2(tan⁡2(x)+1)2log⁡(2x+3)+4(tan⁡2(x)+1)log⁡(2x+3)tan⁡2(x)+12(tan⁡2(x)+1)tan⁡(x)2x+3−12(tan⁡2(x)+1)(2x+3)2+16tan⁡(x)(2x+3)3)\left(2 x + 3\right)^{\tan{\left(x \right)}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} + \frac{2 \tan{\left(x \right)}}{2 x + 3}\right)^{3} + 6 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} + \frac{2 \tan{\left(x \right)}}{2 x + 3}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{2 x + 3} - \frac{2 \tan{\left(x \right)}}{\left(2 x + 3\right)^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 x + 3 \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 x + 3 \right)} \tan^{2}{\left(x \right)} + \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{2 x + 3} - \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(2 x + 3\right)^{2}} + \frac{16 \tan{\left(x \right)}}{\left(2 x + 3\right)^{3}}\right)
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Gráfico
Derivada de (2*x+3)^tan(x)
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