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

Derivada de (x^2+3)^tgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
        tan(x)
/ 2    \      
\x  + 3/
(x2+3)tan⁡(x)\left(x^{2} + 3\right)^{\tan{\left(x \right)}} 
(x^2 + 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
02468-8-6-4-2-101005e43
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        tan(x)                                         
/ 2    \       //       2   \    / 2    \   2*x*tan(x)\
\x  + 3/      *|\1 + tan (x)/*log\x  + 3/ + ----------|
               |                               2      |
               \                              x  + 3  /
(x2+3)tan⁡(x)(2xtan⁡(x)x2+3+(tan⁡2(x)+1)log⁡(x2+3))\left(x^{2} + 3\right)^{\tan{\left(x \right)}} \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 3} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)}\right)
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Segunda derivada [src] 
        tan(x) /                                        2                 2                                                   /       2   \\
/     2\       |//       2   \    /     2\   2*x*tan(x)\    2*tan(x)   4*x *tan(x)     /       2   \    /     2\          4*x*\1 + tan (x)/|
\3 + x /      *||\1 + tan (x)/*log\3 + x / + ----------|  + -------- - ----------- + 2*\1 + tan (x)/*log\3 + x /*tan(x) + -----------------|
               ||                                   2  |          2             2                                                    2     |
               |\                              3 + x   /     3 + x      /     2\                                                3 + x      |
               \                                                        \3 + x /                                                           /
(x2+3)tan⁡(x)(−4x2tan⁡(x)(x2+3)2+4x(tan⁡2(x)+1)x2+3+(2xtan⁡(x)x2+3+(tan⁡2(x)+1)log⁡(x2+3))2+2(tan⁡2(x)+1)log⁡(x2+3)tan⁡(x)+2tan⁡(x)x2+3)\left(x^{2} + 3\right)^{\tan{\left(x \right)}} \left(- \frac{4 x^{2} \tan{\left(x \right)}}{\left(x^{2} + 3\right)^{2}} + \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 3} + \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 3} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)} \tan{\left(x \right)} + \frac{2 \tan{\left(x \right)}}{x^{2} + 3}\right)
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Tercera derivada [src] 
        tan(x) /                                        3                  2                 /       2   \                                              /                                               2              /       2   \\                     2 /       2   \                                             3               /       2   \       \
/     2\       |//       2   \    /     2\   2*x*tan(x)\      /       2   \     /     2\   6*\1 + tan (x)/     //       2   \    /     2\   2*x*tan(x)\ |tan(x)   /       2   \    /     2\          2*x *tan(x)   2*x*\1 + tan (x)/|   12*x*tan(x)   12*x *\1 + tan (x)/        2    /       2   \    /     2\   16*x *tan(x)   12*x*\1 + tan (x)/*tan(x)|
\3 + x /      *||\1 + tan (x)/*log\3 + x / + ----------|  + 2*\1 + tan (x)/ *log\3 + x / + --------------- + 6*|\1 + tan (x)/*log\3 + x / + ----------|*|------ + \1 + tan (x)/*log\3 + x /*tan(x) - ----------- + -----------------| - ----------- - ------------------- + 4*tan (x)*\1 + tan (x)/*log\3 + x / + ------------ + -------------------------|
               ||                                   2  |                                             2         |                                   2  | |     2                                               2               2     |            2                 2                                                       3                    2         |
               |\                              3 + x   /                                        3 + x          \                              3 + x   / |3 + x                                        /     2\           3 + x      |    /     2\          /     2\                                                /     2\                3 + x          |
               \                                                                                                                                        \                                             \3 + x /                      /    \3 + x /          \3 + x /                                                \3 + x /                               /
(x2+3)tan⁡(x)(16x3tan⁡(x)(x2+3)3−12x2(tan⁡2(x)+1)(x2+3)2+12x(tan⁡2(x)+1)tan⁡(x)x2+3−12xtan⁡(x)(x2+3)2+(2xtan⁡(x)x2+3+(tan⁡2(x)+1)log⁡(x2+3))3+6(2xtan⁡(x)x2+3+(tan⁡2(x)+1)log⁡(x2+3))(−2x2tan⁡(x)(x2+3)2+2x(tan⁡2(x)+1)x2+3+(tan⁡2(x)+1)log⁡(x2+3)tan⁡(x)+tan⁡(x)x2+3)+2(tan⁡2(x)+1)2log⁡(x2+3)+4(tan⁡2(x)+1)log⁡(x2+3)tan⁡2(x)+6(tan⁡2(x)+1)x2+3)\left(x^{2} + 3\right)^{\tan{\left(x \right)}} \left(\frac{16 x^{3} \tan{\left(x \right)}}{\left(x^{2} + 3\right)^{3}} - \frac{12 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 3\right)^{2}} + \frac{12 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2} + 3} - \frac{12 x \tan{\left(x \right)}}{\left(x^{2} + 3\right)^{2}} + \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 3} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)}\right)^{3} + 6 \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 3} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)}\right) \left(- \frac{2 x^{2} \tan{\left(x \right)}}{\left(x^{2} + 3\right)^{2}} + \frac{2 x \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 3} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)} \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{x^{2} + 3}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{2} + 3 \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 3 \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 3}\right)
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Gráfico
Derivada de (x^2+3)^tgx
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