Sr Examen

Otras calculadoras

y=ln^5x*arctg7x^4
Derivada de la función/ ln^5x/ arctg/ y=ln^5x*arctg7x^4

Derivada de y=ln^5x*arctg7x^4

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   5        4     
log (x)*atan (7*x)
log⁡(x)5atan⁡4(7x)\log{\left(x \right)}^{5} \operatorname{atan}^{4}{\left(7 x \right)} 
log(x)^5*atan(7*x)^4
Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      4         4             3         5   
5*atan (7*x)*log (x)   28*atan (7*x)*log (x)
-------------------- + ---------------------
         x                           2      
                             1 + 49*x
28log⁡(x)5atan⁡3(7x)49x2+1+5log⁡(x)4atan⁡4(7x)x\frac{28 \log{\left(x \right)}^{5} \operatorname{atan}^{3}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{atan}^{4}{\left(7 x \right)}}{x}
Simplificar
Segunda derivada [src] 
                   /         2                                  2                                          \
    2         3    |  196*log (x)*(-3 + 14*x*atan(7*x))   5*atan (7*x)*(-4 + log(x))   280*atan(7*x)*log(x)|
atan (7*x)*log (x)*|- --------------------------------- - -------------------------- + --------------------|
                   |                        2                          2                    /        2\    |
                   |             /        2\                          x                   x*\1 + 49*x /    |
                   \             \1 + 49*x /                                                               /
(−196(14xatan⁡(7x)−3)log⁡(x)2(49x2+1)2+280log⁡(x)atan⁡(7x)x(49x2+1)−5(log⁡(x)−4)atan⁡2(7x)x2)log⁡(x)3atan⁡2(7x)\left(- \frac{196 \left(14 x \operatorname{atan}{\left(7 x \right)} - 3\right) \log{\left(x \right)}^{2}}{\left(49 x^{2} + 1\right)^{2}} + \frac{280 \log{\left(x \right)} \operatorname{atan}{\left(7 x \right)}}{x \left(49 x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{atan}^{2}{\left(7 x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3} \operatorname{atan}^{2}{\left(7 x \right)}
Simplificar
Tercera derivada [src] 
          /                                                     /                                                 2     2     \                                                                                     \          
          |                                                3    |      2            3       63*x*atan(7*x)   196*x *atan (7*x)|                                                                                     |          
          |                                        1372*log (x)*|- atan (7*x) + --------- - -------------- + -----------------|                                                                                     |          
          |      3      /       2              \                |                       2             2                  2    |           2                                              2                          |          
     2    |5*atan (7*x)*\6 + log (x) - 6*log(x)/                \               1 + 49*x      1 + 49*x           1 + 49*x     /   1470*log (x)*(-3 + 14*x*atan(7*x))*atan(7*x)   210*atan (7*x)*(-4 + log(x))*log(x)|          
2*log (x)*|------------------------------------- + ---------------------------------------------------------------------------- - -------------------------------------------- - -----------------------------------|*atan(7*x)
          |                   3                                                               2                                                               2                              2 /        2\          |          
          |                  x                                                     /        2\                                                     /        2\                              x *\1 + 49*x /          |          
          \                                                                        \1 + 49*x /                                                   x*\1 + 49*x /                                                      /
2(1372(196x2atan⁡2(7x)49x2+1−63xatan⁡(7x)49x2+1−atan⁡2(7x)+349x2+1)log⁡(x)3(49x2+1)2−1470(14xatan⁡(7x)−3)log⁡(x)2atan⁡(7x)x(49x2+1)2−210(log⁡(x)−4)log⁡(x)atan⁡2(7x)x2(49x2+1)+5(log⁡(x)2−6log⁡(x)+6)atan⁡3(7x)x3)log⁡(x)2atan⁡(7x)2 \left(\frac{1372 \left(\frac{196 x^{2} \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} - \frac{63 x \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} - \operatorname{atan}^{2}{\left(7 x \right)} + \frac{3}{49 x^{2} + 1}\right) \log{\left(x \right)}^{3}}{\left(49 x^{2} + 1\right)^{2}} - \frac{1470 \left(14 x \operatorname{atan}{\left(7 x \right)} - 3\right) \log{\left(x \right)}^{2} \operatorname{atan}{\left(7 x \right)}}{x \left(49 x^{2} + 1\right)^{2}} - \frac{210 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{atan}^{2}{\left(7 x \right)}}{x^{2} \left(49 x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{atan}^{3}{\left(7 x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2} \operatorname{atan}{\left(7 x \right)}
Simplificar
Gráfico
Derivada de y=ln^5x*arctg7x^4
    © Sr Examen – Калькулятор