Sr Examen

Otras calculadoras

Derivada de xlnx+arcsinx^(1/2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
             _________
x*log(x) + \/ asin(x) 
$$x \log{\left(x \right)} + \sqrt{\operatorname{asin}{\left(x \right)}}$$
x*log(x) + sqrt(asin(x))
Gráfica
Primera derivada [src]
                1                     
1 + ------------------------- + log(x)
         ________                     
        /      2    _________         
    2*\/  1 - x  *\/ asin(x)          
$$\log{\left(x \right)} + 1 + \frac{1}{2 \sqrt{1 - x^{2}} \sqrt{\operatorname{asin}{\left(x \right)}}}$$
Segunda derivada [src]
1             1                          x            
- + ---------------------- + -------------------------
x     /      2\     3/2                3/2            
    4*\-1 + x /*asin   (x)     /     2\      _________
                             2*\1 - x /   *\/ asin(x) 
$$\frac{x}{2 \left(1 - x^{2}\right)^{\frac{3}{2}} \sqrt{\operatorname{asin}{\left(x \right)}}} + \frac{1}{4 \left(x^{2} - 1\right) \operatorname{asin}^{\frac{3}{2}}{\left(x \right)}} + \frac{1}{x}$$
Tercera derivada [src]
                                                                                                      2          
  1                1                          3                         3*x                        3*x           
- -- + ------------------------- + ------------------------ - ----------------------- + -------------------------
   2             3/2                         3/2                         2                        5/2            
  x      /     2\      _________     /     2\        5/2        /      2\      3/2        /     2\      _________
       2*\1 - x /   *\/ asin(x)    8*\1 - x /   *asin   (x)   4*\-1 + x / *asin   (x)   2*\1 - x /   *\/ asin(x) 
$$\frac{3 x^{2}}{2 \left(1 - x^{2}\right)^{\frac{5}{2}} \sqrt{\operatorname{asin}{\left(x \right)}}} - \frac{3 x}{4 \left(x^{2} - 1\right)^{2} \operatorname{asin}^{\frac{3}{2}}{\left(x \right)}} + \frac{1}{2 \left(1 - x^{2}\right)^{\frac{3}{2}} \sqrt{\operatorname{asin}{\left(x \right)}}} + \frac{3}{8 \left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{\frac{5}{2}}{\left(x \right)}} - \frac{1}{x^{2}}$$