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x*(ln(arctg(7x)))+(4x+1)/((tg(x)^3)+1)
Derivada de la función/ x*(ln(arctg(7x)))+(4x+1)/((tg(x)^3)+1)

Derivada de x*(ln(arctg(7x)))+(4x+1)/((tg(x)^3)+1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                     4*x + 1  
x*log(atan(7*x)) + -----------
                      3       
                   tan (x) + 1
xlog⁡(atan⁡(7x))+4x+1tan⁡3(x)+1x \log{\left(\operatorname{atan}{\left(7 x \right)} \right)} + \frac{4 x + 1}{\tan^{3}{\left(x \right)} + 1} 
x*log(atan(7*x)) + (4*x + 1)/(tan(x)^3 + 1)
Gráfica
02468-8-6-4-2-1010-25002500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                         2    /         2   \                           
     4                 7*x            tan (x)*\3 + 3*tan (x)/*(4*x + 1)                 
----------- + --------------------- - --------------------------------- + log(atan(7*x))
   3          /        2\                                    2                          
tan (x) + 1   \1 + 49*x /*atan(7*x)             /   3       \                           
                                                \tan (x) + 1/
7x(49x2+1)atan⁡(7x)−(4x+1)(3tan⁡2(x)+3)tan⁡2(x)(tan⁡3(x)+1)2+log⁡(atan⁡(7x))+4tan⁡3(x)+1\frac{7 x}{\left(49 x^{2} + 1\right) \operatorname{atan}{\left(7 x \right)}} - \frac{\left(4 x + 1\right) \left(3 \tan^{2}{\left(x \right)} + 3\right) \tan^{2}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} + \log{\left(\operatorname{atan}{\left(7 x \right)} \right)} + \frac{4}{\tan^{3}{\left(x \right)} + 1}
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Segunda derivada [src] 
                                                                                                                     2                                                                        2                  
                                     2                                           2    /       2   \     /       2   \                          3    /       2   \                /       2   \     4             
          14                    686*x                      49*x            24*tan (x)*\1 + tan (x)/   6*\1 + tan (x)/ *(1 + 4*x)*tan(x)   6*tan (x)*\1 + tan (x)/*(1 + 4*x)   18*\1 + tan (x)/ *tan (x)*(1 + 4*x)
--------------------- - ---------------------- - ----------------------- - ------------------------ - --------------------------------- - --------------------------------- + -----------------------------------
/        2\                        2                        2                                2                               2                                   2                                    3          
\1 + 49*x /*atan(7*x)   /        2\              /        2\      2             /       3   \                   /       3   \                       /       3   \                        /       3   \           
                        \1 + 49*x / *atan(7*x)   \1 + 49*x / *atan (7*x)        \1 + tan (x)/                   \1 + tan (x)/                       \1 + tan (x)/                        \1 + tan (x)/
−686x2(49x2+1)2atan⁡(7x)−49x(49x2+1)2atan⁡2(7x)−6(4x+1)(tan⁡2(x)+1)2tan⁡(x)(tan⁡3(x)+1)2+18(4x+1)(tan⁡2(x)+1)2tan⁡4(x)(tan⁡3(x)+1)3−6(4x+1)(tan⁡2(x)+1)tan⁡3(x)(tan⁡3(x)+1)2−24(tan⁡2(x)+1)tan⁡2(x)(tan⁡3(x)+1)2+14(49x2+1)atan⁡(7x)- \frac{686 x^{2}}{\left(49 x^{2} + 1\right)^{2} \operatorname{atan}{\left(7 x \right)}} - \frac{49 x}{\left(49 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(7 x \right)}} - \frac{6 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} + \frac{18 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{4}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{3}} - \frac{6 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{3}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} - \frac{24 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} + \frac{14}{\left(49 x^{2} + 1\right) \operatorname{atan}{\left(7 x \right)}}
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Tercera derivada [src] 
                                                                     2                                                    3                              2                                                                                                         3                                     2                                                                           2                                      3                  
                                                        /       2   \                 3    /       2   \     /       2   \                  /       2   \     4                                               2                        3              /       2   \     6                   /       2   \     2                      4    /       2   \                 /       2   \     5                    /       2   \     3             
            147                     2744*x           72*\1 + tan (x)/ *tan(x)   72*tan (x)*\1 + tan (x)/   6*\1 + tan (x)/ *(1 + 4*x)   216*\1 + tan (x)/ *tan (x)            686*x                    14406*x                 134456*x           162*\1 + tan (x)/ *tan (x)*(1 + 4*x)   42*\1 + tan (x)/ *tan (x)*(1 + 4*x)   12*tan (x)*\1 + tan (x)/*(1 + 4*x)   108*\1 + tan (x)/ *tan (x)*(1 + 4*x)   108*\1 + tan (x)/ *tan (x)*(1 + 4*x)
- ----------------------- - ---------------------- - ------------------------ - ------------------------ - -------------------------- + -------------------------- + ----------------------- + ----------------------- + ---------------------- - ------------------------------------ - ----------------------------------- - ---------------------------------- + ------------------------------------ + ------------------------------------
             2                         2                               2                          2                           2                            3                    3                         3                         3                                     4                                      2                                    2                                     3                                      3           
  /        2\      2        /        2\                   /       3   \              /       3   \               /       3   \                /       3   \          /        2\      3        /        2\      2        /        2\                         /       3   \                          /       3   \                        /       3   \                         /       3   \                          /       3   \            
  \1 + 49*x / *atan (7*x)   \1 + 49*x / *atan(7*x)        \1 + tan (x)/              \1 + tan (x)/               \1 + tan (x)/                \1 + tan (x)/          \1 + 49*x / *atan (7*x)   \1 + 49*x / *atan (7*x)   \1 + 49*x / *atan(7*x)              \1 + tan (x)/                          \1 + tan (x)/                        \1 + tan (x)/                         \1 + tan (x)/                          \1 + tan (x)/
134456x3(49x2+1)3atan⁡(7x)+14406x2(49x2+1)3atan⁡2(7x)−2744x(49x2+1)2atan⁡(7x)+686x(49x2+1)3atan⁡3(7x)−6(4x+1)(tan⁡2(x)+1)3(tan⁡3(x)+1)2+108(4x+1)(tan⁡2(x)+1)3tan⁡3(x)(tan⁡3(x)+1)3−162(4x+1)(tan⁡2(x)+1)3tan⁡6(x)(tan⁡3(x)+1)4−42(4x+1)(tan⁡2(x)+1)2tan⁡2(x)(tan⁡3(x)+1)2+108(4x+1)(tan⁡2(x)+1)2tan⁡5(x)(tan⁡3(x)+1)3−12(4x+1)(tan⁡2(x)+1)tan⁡4(x)(tan⁡3(x)+1)2−72(tan⁡2(x)+1)2tan⁡(x)(tan⁡3(x)+1)2+216(tan⁡2(x)+1)2tan⁡4(x)(tan⁡3(x)+1)3−72(tan⁡2(x)+1)tan⁡3(x)(tan⁡3(x)+1)2−147(49x2+1)2atan⁡2(7x)\frac{134456 x^{3}}{\left(49 x^{2} + 1\right)^{3} \operatorname{atan}{\left(7 x \right)}} + \frac{14406 x^{2}}{\left(49 x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(7 x \right)}} - \frac{2744 x}{\left(49 x^{2} + 1\right)^{2} \operatorname{atan}{\left(7 x \right)}} + \frac{686 x}{\left(49 x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(7 x \right)}} - \frac{6 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} + \frac{108 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \tan^{3}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{3}} - \frac{162 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \tan^{6}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{4}} - \frac{42 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} + \frac{108 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{5}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{3}} - \frac{12 \left(4 x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} - \frac{72 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} + \frac{216 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{4}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{3}} - \frac{72 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{3}{\left(x \right)}}{\left(\tan^{3}{\left(x \right)} + 1\right)^{2}} - \frac{147}{\left(49 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(7 x \right)}}
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Gráfico
Derivada de x*(ln(arctg(7x)))+(4x+1)/((tg(x)^3)+1)
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