Sr Examen

Otras calculadoras


y=arctanlnx^3+x^(1/3)

Derivada de y=arctanlnx^3+x^(1/3)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
           3      3 ___
atan(x)*log (x) + \/ x 
$$\sqrt[3]{x} + \log{\left(x \right)}^{3} \operatorname{atan}{\left(x \right)}$$
atan(x)*log(x)^3 + x^(1/3)
Gráfica
Primera derivada [src]
            3           2           
  1      log (x)   3*log (x)*atan(x)
------ + ------- + -----------------
   2/3         2           x        
3*x       1 + x                     
$$\frac{\log{\left(x \right)}^{3}}{x^{2} + 1} + \frac{3 \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{x} + \frac{1}{3 x^{\frac{2}{3}}}$$
Segunda derivada [src]
                2                     3           2                       
    2      3*log (x)*atan(x)   2*x*log (x)   6*log (x)    6*atan(x)*log(x)
- ------ - ----------------- - ----------- + ---------- + ----------------
     5/3            2                   2      /     2\           2       
  9*x              x            /     2\     x*\1 + x /          x        
                                \1 + x /                                  
$$- \frac{2 x \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{2}} + \frac{6 \log{\left(x \right)}^{2}}{x \left(x^{2} + 1\right)} - \frac{3 \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{x^{2}} + \frac{6 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}} - \frac{2}{9 x^{\frac{5}{3}}}$$
Tercera derivada [src]
                2           3                                            2            2                 2    3                 
   10     18*log (x)   2*log (x)   6*atan(x)   18*atan(x)*log(x)    9*log (x)    6*log (x)*atan(x)   8*x *log (x)    18*log(x) 
------- - ---------- - --------- + --------- - ----------------- - ----------- + ----------------- + ------------ + -----------
    8/3           2            2        3               3           2 /     2\            3                   3      2 /     2\
27*x      /     2\     /     2\        x               x           x *\1 + x /           x            /     2\      x *\1 + x /
          \1 + x /     \1 + x /                                                                       \1 + x /                 
$$\frac{8 x^{2} \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{3}} - \frac{2 \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{18 \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{9 \log{\left(x \right)}^{2}}{x^{2} \left(x^{2} + 1\right)} + \frac{18 \log{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{6 \log{\left(x \right)}^{2} \operatorname{atan}{\left(x \right)}}{x^{3}} - \frac{18 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{3}} + \frac{6 \operatorname{atan}{\left(x \right)}}{x^{3}} + \frac{10}{27 x^{\frac{8}{3}}}$$
Gráfico
Derivada de y=arctanlnx^3+x^(1/3)