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x^tgx*arctg(x^2)

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  • Derivada de:
  • Derivada de i*n*sin(x)
  • Derivada de i*n*x
  • Derivada de 3^-x Derivada de 3^-x
  • Derivada de y=6x Derivada de y=6x

  • Expresiones idénticas

  • x^tgx*arctg(x^ dos)
  • x en el grado tgx multiplicar por arctg(x al cuadrado )
  • x en el grado tgx multiplicar por arctg(x en el grado dos)
  • xtgx*arctg(x2)
  • xtgx*arctgx2
  • x^tgx*arctg(x²)
  • x en el grado tgx*arctg(x en el grado 2)
  • x^tgxarctg(x^2)
  • xtgxarctg(x2)
  • xtgxarctgx2
  • x^tgxarctgx^2
Derivada de la función/ x^tgx/ (x^2)/ arctg/ x^tgx*arctg(x^2)

Derivada de x^tgx*arctg(x^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 tan(x)     / 2\
x      *atan\x /
xtan⁡(x)atan⁡(x2)x^{\tan{\left(x \right)}} \operatorname{atan}{\left(x^{2} \right)} 
x^tan(x)*atan(x^2)
Gráfica
02468-8-6-4-2-10100500000000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                        tan(x)
 tan(x) /tan(x)   /       2   \       \     / 2\   2*x*x      
x      *|------ + \1 + tan (x)/*log(x)|*atan\x / + -----------
        \  x                          /                    4  
                                                      1 + x
2xxtan⁡(x)x4+1+xtan⁡(x)((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)atan⁡(x2)\frac{2 x x^{\tan{\left(x \right)}}}{x^{4} + 1} + x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x^{2} \right)}
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Segunda derivada [src] 
        /                                                                                                           /         4 \                                      \
        |                                                                                                           |      4*x  |                                      |
        |                                                                                                         2*|-1 + ------|       /tan(x)   /       2   \       \|
        |/                               2              /       2   \                                \              |          4|   4*x*|------ + \1 + tan (x)/*log(x)||
 tan(x) ||/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |     / 2\     \     1 + x /       \  x                          /|
x      *|||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*atan\x / - --------------- + -----------------------------------|
        ||\  x                          /       2            x                                       |                      4                           4              |
        \\                                     x                                                     /                 1 + x                       1 + x               /
xtan⁡(x)(4x((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)x4+1+(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)atan⁡(x2)−2(4x4x4+1−1)x4+1)x^{\tan{\left(x \right)}} \left(\frac{4 x \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{x^{4} + 1} + \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x^{2} \right)} - \frac{2 \left(\frac{4 x^{4}}{x^{4} + 1} - 1\right)}{x^{4} + 1}\right)
Simplificar
Tercera derivada [src] 
        /                                                                                                                                                                                                                                                                  /         4 \                                       /                               2              /       2   \                                \        /         4 \\
        |                                                                                                                                                                                                                                                                  |      4*x  | /tan(x)   /       2   \       \       |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |      3 |      8*x  ||
        |                                                                                                                                                                                                                                                                6*|-1 + ------|*|------ + \1 + tan (x)/*log(x)|   6*x*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|   8*x *|-5 + ------||
        |/                               3     /       2   \                             2                                            /             /       2   \                                \                                      /       2   \       \              |          4| \  x                          /       |\  x                          /       2            x                                       |        |          4||
 tan(x) ||/tan(x)   /       2   \       \    3*\1 + tan (x)/   2*tan(x)     /       2   \             /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |        2    /       2   \          6*\1 + tan (x)/*tan(x)|     / 2\     \     1 + x /                                       \                                     x                                                     /        \     1 + x /|
x      *|||------ + \1 + tan (x)/*log(x)|  - --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------|*atan\x / - ----------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------|
        ||\  x                          /            2             3                                  \  x                          / |     2            x                                       |                                              x           |                                      4                                                                          4                                                            2     |
        |\                                          x             x                                                                   \    x                                                     /                                                          /                                 1 + x                                                                      1 + x                                                     /     4\      |
        \                                                                                                                                                                                                                                                                                                                                                                                                                          \1 + x /      /
xtan⁡(x)(8x3(8x4x4+1−5)(x4+1)2+6x(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)x4+1+(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)3+3((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)+2(tan⁡2(x)+1)2log⁡(x)+4(tan⁡2(x)+1)log⁡(x)tan⁡2(x)+6(tan⁡2(x)+1)tan⁡(x)x−3(tan⁡2(x)+1)x2+2tan⁡(x)x3)atan⁡(x2)−6(4x4x4+1−1)((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)x4+1)x^{\tan{\left(x \right)}} \left(\frac{8 x^{3} \left(\frac{8 x^{4}}{x^{4} + 1} - 5\right)}{\left(x^{4} + 1\right)^{2}} + \frac{6 x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x^{4} + 1} + \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}\right) \operatorname{atan}{\left(x^{2} \right)} - \frac{6 \left(\frac{4 x^{4}}{x^{4} + 1} - 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{x^{4} + 1}\right)
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Gráfico
Derivada de x^tgx*arctg(x^2)
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