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atan(log(x))+log(atan(x))
Derivada de la función/ tan(x)/ log(x)/ atan(log(x))+log(atan(x))

Derivada de atan(log(x))+log(atan(x))

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

Gráfico:

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Solución

Ha introducido [src] 
atan(log(x)) + log(atan(x))
log⁡(atan⁡(x))+atan⁡(log⁡(x))\log{\left(\operatorname{atan}{\left(x \right)} \right)} + \operatorname{atan}{\left(\log{\left(x \right)} \right)} 
atan(log(x)) + log(atan(x))
Gráfica
02468-8-6-4-2-1010-2020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       1                 1        
--------------- + ----------------
  /       2   \   /     2\        
x*\1 + log (x)/   \1 + x /*atan(x)
1(x2+1)atan⁡(x)+1x(log⁡(x)2+1)\frac{1}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}
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Segunda derivada [src] 
 /       1                   1                   2*x               2*log(x)    \
-|---------------- + ------------------ + ----------------- + -----------------|
 | 2 /       2   \           2                    2                           2|
 |x *\1 + log (x)/   /     2\      2      /     2\             2 /       2   \ |
 \                   \1 + x / *atan (x)   \1 + x / *atan(x)   x *\1 + log (x)/ /
−(2x(x2+1)2atan⁡(x)+1(x2+1)2atan⁡2(x)+1x2(log⁡(x)2+1)+2log⁡(x)x2(log⁡(x)2+1)2)- (\frac{2 x}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} + \frac{1}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{2 \log{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)^{2}})
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Tercera derivada [src] 
  /                                                                                                                                  2                    2      \
  |       1                   1                    1                   1                  3*x                3*log(x)           4*log (x)              4*x       |
2*|---------------- + ------------------ - ----------------- - ----------------- + ------------------ + ----------------- + ----------------- + -----------------|
  | 3 /       2   \           3                            2           2                   3                            2                   3           3        |
  |x *\1 + log (x)/   /     2\      3       3 /       2   \    /     2\            /     2\      2       3 /       2   \     3 /       2   \    /     2\         |
  \                   \1 + x / *atan (x)   x *\1 + log (x)/    \1 + x / *atan(x)   \1 + x / *atan (x)   x *\1 + log (x)/    x *\1 + log (x)/    \1 + x / *atan(x)/
2(4x2(x2+1)3atan⁡(x)+3x(x2+1)3atan⁡2(x)−1(x2+1)2atan⁡(x)+1(x2+1)3atan⁡3(x)+1x3(log⁡(x)2+1)+3log⁡(x)x3(log⁡(x)2+1)2−1x3(log⁡(x)2+1)2+4log⁡(x)2x3(log⁡(x)2+1)3)2 \left(\frac{4 x^{2}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}{\left(x \right)}} + \frac{3 x}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(x \right)}} - \frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{1}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(x \right)}} + \frac{1}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{3 \log{\left(x \right)}}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} - \frac{1}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} + \frac{4 \log{\left(x \right)}^{2}}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)^{3}}\right)
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Gráfico
Derivada de atan(log(x))+log(atan(x))
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