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x*tg(x*x+1)*ln(x+1)
Derivada de la función/ (x+1)/ x*x+1/ x*tg(x*x+1)*ln(x+1)

Derivada de x*tg(x*x+1)*ln(x+1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
x*tan(x*x + 1)*log(x + 1)
xtan⁡(xx+1)log⁡(x+1)x \tan{\left(x x + 1 \right)} \log{\left(x + 1 \right)} 
(x*tan(x*x + 1))*log(x + 1)
Gráfica
02468-8-6-4-2-1010-200000200000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/   2 /       2         \               \              x*tan(x*x + 1)
\2*x *\1 + tan (x*x + 1)/ + tan(x*x + 1)/*log(x + 1) + --------------
                                                           x + 1
xtan⁡(xx+1)x+1+(2x2(tan⁡2(xx+1)+1)+tan⁡(xx+1))log⁡(x+1)\frac{x \tan{\left(x x + 1 \right)}}{x + 1} + \left(2 x^{2} \left(\tan^{2}{\left(x x + 1 \right)} + 1\right) + \tan{\left(x x + 1 \right)}\right) \log{\left(x + 1 \right)}
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Segunda derivada [src] 
  /   2 /       2/     2\\      /     2\\        /     2\                                                                            
2*\2*x *\1 + tan \1 + x // + tan\1 + x //   x*tan\1 + x /       /         2/     2\      2 /       2/     2\\    /     2\\           
----------------------------------------- - ------------- + 2*x*\3 + 3*tan \1 + x / + 4*x *\1 + tan \1 + x //*tan\1 + x //*log(1 + x)
                  1 + x                               2                                                                              
                                               (1 + x)
2x(4x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+3tan⁡2(x2+1)+3)log⁡(x+1)−xtan⁡(x2+1)(x+1)2+2(2x2(tan⁡2(x2+1)+1)+tan⁡(x2+1))x+12 x \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + 3 \tan^{2}{\left(x^{2} + 1 \right)} + 3\right) \log{\left(x + 1 \right)} - \frac{x \tan{\left(x^{2} + 1 \right)}}{\left(x + 1\right)^{2}} + \frac{2 \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + \tan{\left(x^{2} + 1 \right)}\right)}{x + 1}
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Tercera derivada [src] 
    /   2 /       2/     2\\      /     2\\                                                                                                                                                                             /     2\       /         2/     2\      2 /       2/     2\\    /     2\\
  3*\2*x *\1 + tan \1 + x // + tan\1 + x //     /         2/     2\      2 /       2/     2\\ /     /     2\      2 /       2/     2\\      2    2/     2\\       2 /       2/     2\\    /     2\\              2*x*tan\1 + x /   6*x*\3 + 3*tan \1 + x / + 4*x *\1 + tan \1 + x //*tan\1 + x //
- ----------------------------------------- + 2*\3 + 3*tan \1 + x / + 4*x *\1 + tan \1 + x //*\3*tan\1 + x / + 2*x *\1 + tan \1 + x // + 4*x *tan \1 + x // + 12*x *\1 + tan \1 + x //*tan\1 + x //*log(1 + x) + --------------- + --------------------------------------------------------------
                          2                                                                                                                                                                                                 3                                  1 + x                             
                   (1 + x)                                                                                                                                                                                           (1 + x)
6x(4x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+3tan⁡2(x2+1)+3)x+1+2xtan⁡(x2+1)(x+1)3+2(4x2(tan⁡2(x2+1)+1)(2x2(tan⁡2(x2+1)+1)+4x2tan⁡2(x2+1)+3tan⁡(x2+1))+12x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+3tan⁡2(x2+1)+3)log⁡(x+1)−3(2x2(tan⁡2(x2+1)+1)+tan⁡(x2+1))(x+1)2\frac{6 x \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + 3 \tan^{2}{\left(x^{2} + 1 \right)} + 3\right)}{x + 1} + \frac{2 x \tan{\left(x^{2} + 1 \right)}}{\left(x + 1\right)^{3}} + 2 \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + 4 x^{2} \tan^{2}{\left(x^{2} + 1 \right)} + 3 \tan{\left(x^{2} + 1 \right)}\right) + 12 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + 3 \tan^{2}{\left(x^{2} + 1 \right)} + 3\right) \log{\left(x + 1 \right)} - \frac{3 \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + \tan{\left(x^{2} + 1 \right)}\right)}{\left(x + 1\right)^{2}}
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3-я производная [src] 
    /   2 /       2/     2\\      /     2\\                                                                                                                                                                             /     2\       /         2/     2\      2 /       2/     2\\    /     2\\
  3*\2*x *\1 + tan \1 + x // + tan\1 + x //     /         2/     2\      2 /       2/     2\\ /     /     2\      2 /       2/     2\\      2    2/     2\\       2 /       2/     2\\    /     2\\              2*x*tan\1 + x /   6*x*\3 + 3*tan \1 + x / + 4*x *\1 + tan \1 + x //*tan\1 + x //
- ----------------------------------------- + 2*\3 + 3*tan \1 + x / + 4*x *\1 + tan \1 + x //*\3*tan\1 + x / + 2*x *\1 + tan \1 + x // + 4*x *tan \1 + x // + 12*x *\1 + tan \1 + x //*tan\1 + x //*log(1 + x) + --------------- + --------------------------------------------------------------
                          2                                                                                                                                                                                                 3                                  1 + x                             
                   (1 + x)                                                                                                                                                                                           (1 + x)
6x(4x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+3tan⁡2(x2+1)+3)x+1+2xtan⁡(x2+1)(x+1)3+2(4x2(tan⁡2(x2+1)+1)(2x2(tan⁡2(x2+1)+1)+4x2tan⁡2(x2+1)+3tan⁡(x2+1))+12x2(tan⁡2(x2+1)+1)tan⁡(x2+1)+3tan⁡2(x2+1)+3)log⁡(x+1)−3(2x2(tan⁡2(x2+1)+1)+tan⁡(x2+1))(x+1)2\frac{6 x \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + 3 \tan^{2}{\left(x^{2} + 1 \right)} + 3\right)}{x + 1} + \frac{2 x \tan{\left(x^{2} + 1 \right)}}{\left(x + 1\right)^{3}} + 2 \left(4 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + 4 x^{2} \tan^{2}{\left(x^{2} + 1 \right)} + 3 \tan{\left(x^{2} + 1 \right)}\right) + 12 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) \tan{\left(x^{2} + 1 \right)} + 3 \tan^{2}{\left(x^{2} + 1 \right)} + 3\right) \log{\left(x + 1 \right)} - \frac{3 \left(2 x^{2} \left(\tan^{2}{\left(x^{2} + 1 \right)} + 1\right) + \tan{\left(x^{2} + 1 \right)}\right)}{\left(x + 1\right)^{2}}
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Gráfico
Derivada de x*tg(x*x+1)*ln(x+1)
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