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x+ln(x^2+tg(x+4x^2))
Derivada de la función/ x+ln(x^2+tg(x+4x^2))

Derivada de x+ln(x^2+tg(x+4x^2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
       / 2      /       2\\
x + log\x  + tan\x + 4*x //
x+log⁡(x2+tan⁡(4x2+x))x + \log{\left(x^{2} + \tan{\left(4 x^{2} + x \right)} \right)} 
x + log(x^2 + tan(x + 4*x^2))
Gráfica
02468-8-6-4-2-1010-250000250000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          /       2/       2\\          
    2*x + \1 + tan \x + 4*x //*(1 + 8*x)
1 + ------------------------------------
              2      /       2\         
             x  + tan\x + 4*x /
2x+(8x+1)(tan⁡2(4x2+x)+1)x2+tan⁡(4x2+x)+1\frac{2 x + \left(8 x + 1\right) \left(\tan^{2}{\left(4 x^{2} + x \right)} + 1\right)}{x^{2} + \tan{\left(4 x^{2} + x \right)}} + 1
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Segunda derivada [src] 
                                                                    2                                                        
                           /      /       2             \          \                                                         
          2                \2*x + \1 + tan (x*(1 + 4*x))/*(1 + 8*x)/               2 /       2             \                 
10 + 8*tan (x*(1 + 4*x)) - ------------------------------------------ + 2*(1 + 8*x) *\1 + tan (x*(1 + 4*x))/*tan(x*(1 + 4*x))
                                      2                                                                                      
                                     x  + tan(x*(1 + 4*x))                                                                   
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                                                     2                                                                       
                                                    x  + tan(x*(1 + 4*x))
−(2x+(8x+1)(tan⁡2(x(4x+1))+1))2x2+tan⁡(x(4x+1))+2(8x+1)2(tan⁡2(x(4x+1))+1)tan⁡(x(4x+1))+8tan⁡2(x(4x+1))+10x2+tan⁡(x(4x+1))\frac{- \frac{\left(2 x + \left(8 x + 1\right) \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right)\right)^{2}}{x^{2} + \tan{\left(x \left(4 x + 1\right) \right)}} + 2 \left(8 x + 1\right)^{2} \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right) \tan{\left(x \left(4 x + 1\right) \right)} + 8 \tan^{2}{\left(x \left(4 x + 1\right) \right)} + 10}{x^{2} + \tan{\left(x \left(4 x + 1\right) \right)}}
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Tercera derivada [src] 
  /                                         3                                                                                                                                                                                                                                                              \
  |/      /       2             \          \                                                                                                                                      /      /       2             \          \ /         2                         2 /       2             \                 \|
  |\2*x + \1 + tan (x*(1 + 4*x))/*(1 + 8*x)/    /       2             \           /                               2 /       2             \              2    2             \   3*\2*x + \1 + tan (x*(1 + 4*x))/*(1 + 8*x)/*\5 + 4*tan (x*(1 + 4*x)) + (1 + 8*x) *\1 + tan (x*(1 + 4*x))/*tan(x*(1 + 4*x))/|
2*|------------------------------------------ + \1 + tan (x*(1 + 4*x))/*(1 + 8*x)*\24*tan(x*(1 + 4*x)) + (1 + 8*x) *\1 + tan (x*(1 + 4*x))/ + 2*(1 + 8*x) *tan (x*(1 + 4*x))/ - ---------------------------------------------------------------------------------------------------------------------------|
  |                                2                                                                                                                                                                                                2                                                                      |
  |         / 2                   \                                                                                                                                                                                                x  + tan(x*(1 + 4*x))                                                   |
  \         \x  + tan(x*(1 + 4*x))/                                                                                                                                                                                                                                                                        /
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                                                                                                                                            2                                                                                                                                                               
                                                                                                                                           x  + tan(x*(1 + 4*x))
2((2x+(8x+1)(tan⁡2(x(4x+1))+1))3(x2+tan⁡(x(4x+1)))2−3(2x+(8x+1)(tan⁡2(x(4x+1))+1))((8x+1)2(tan⁡2(x(4x+1))+1)tan⁡(x(4x+1))+4tan⁡2(x(4x+1))+5)x2+tan⁡(x(4x+1))+(8x+1)(tan⁡2(x(4x+1))+1)((8x+1)2(tan⁡2(x(4x+1))+1)+2(8x+1)2tan⁡2(x(4x+1))+24tan⁡(x(4x+1))))x2+tan⁡(x(4x+1))\frac{2 \left(\frac{\left(2 x + \left(8 x + 1\right) \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right)\right)^{3}}{\left(x^{2} + \tan{\left(x \left(4 x + 1\right) \right)}\right)^{2}} - \frac{3 \left(2 x + \left(8 x + 1\right) \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right)\right) \left(\left(8 x + 1\right)^{2} \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right) \tan{\left(x \left(4 x + 1\right) \right)} + 4 \tan^{2}{\left(x \left(4 x + 1\right) \right)} + 5\right)}{x^{2} + \tan{\left(x \left(4 x + 1\right) \right)}} + \left(8 x + 1\right) \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right) \left(\left(8 x + 1\right)^{2} \left(\tan^{2}{\left(x \left(4 x + 1\right) \right)} + 1\right) + 2 \left(8 x + 1\right)^{2} \tan^{2}{\left(x \left(4 x + 1\right) \right)} + 24 \tan{\left(x \left(4 x + 1\right) \right)}\right)\right)}{x^{2} + \tan{\left(x \left(4 x + 1\right) \right)}}
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Gráfico
Derivada de x+ln(x^2+tg(x+4x^2))
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