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y=x×arctg^35x+lntgx
Derivada de la función/ x+lnt/ lntgx/ arctg/ y=x×arctg^35x+lntgx

Derivada de y=x×arctg^35x+lntgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
      35                 
x*atan  (x) + log(tan(x))
xatan⁡35(x)+log⁡(tan⁡(x))x \operatorname{atan}^{35}{\left(x \right)} + \log{\left(\tan{\left(x \right)} \right)} 
x*atan(x)^35 + log(tan(x))
Gráfica
02468-8-6-4-2-1010-1000000010000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                   2               34   
    35      1 + tan (x)   35*x*atan  (x)
atan  (x) + ----------- + --------------
               tan(x)              2    
                              1 + x
35xatan⁡34(x)x2+1+tan⁡2(x)+1tan⁡(x)+atan⁡35(x)\frac{35 x \operatorname{atan}^{34}{\left(x \right)}}{x^{2} + 1} + \frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \operatorname{atan}^{35}{\left(x \right)}
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Segunda derivada [src] 
                             2                                                    
                /       2   \           34          2     34                 33   
         2      \1 + tan (x)/    70*atan  (x)   70*x *atan  (x)   1190*x*atan  (x)
2 + 2*tan (x) - -------------- + ------------ - --------------- + ----------------
                      2                  2                 2                 2    
                   tan (x)          1 + x          /     2\          /     2\     
                                                   \1 + x /          \1 + x /
−70x2atan⁡34(x)(x2+1)2+1190xatan⁡33(x)(x2+1)2−(tan⁡2(x)+1)2tan⁡2(x)+2tan⁡2(x)+2+70atan⁡34(x)x2+1- \frac{70 x^{2} \operatorname{atan}^{34}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{1190 x \operatorname{atan}^{33}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 2 \tan^{2}{\left(x \right)} + 2 + \frac{70 \operatorname{atan}^{34}{\left(x \right)}}{x^{2} + 1}
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Tercera derivada [src] 
  /             3                  2                                                                                                                       \
  |/       2   \      /       2   \                                      33            2     33                34           3     34                  32   |
  |\1 + tan (x)/    2*\1 + tan (x)/      /       2   \          1785*atan  (x)   3570*x *atan  (x)   140*x*atan  (x)   140*x *atan  (x)   19635*x*atan  (x)|
2*|-------------- - ---------------- + 2*\1 + tan (x)/*tan(x) + -------------- - ----------------- - --------------- + ---------------- + -----------------|
  |      3               tan(x)                                           2                  3                  2                 3                   3    |
  |   tan (x)                                                     /     2\           /     2\           /     2\          /     2\            /     2\     |
  \                                                               \1 + x /           \1 + x /           \1 + x /          \1 + x /            \1 + x /     /
2(140x3atan⁡34(x)(x2+1)3−3570x2atan⁡33(x)(x2+1)3−140xatan⁡34(x)(x2+1)2+19635xatan⁡32(x)(x2+1)3+(tan⁡2(x)+1)3tan⁡3(x)−2(tan⁡2(x)+1)2tan⁡(x)+2(tan⁡2(x)+1)tan⁡(x)+1785atan⁡33(x)(x2+1)2)2 \left(\frac{140 x^{3} \operatorname{atan}^{34}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{3570 x^{2} \operatorname{atan}^{33}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{140 x \operatorname{atan}^{34}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{19635 x \operatorname{atan}^{32}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \frac{1785 \operatorname{atan}^{33}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=x×arctg^35x+lntgx
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