Sr Examen

Otras calculadoras

y=lnarcsin(x)×(2/cbrt(x))
Derivada de la función/ sin(x)/ arcsin/ cbrt(x)/ y=lnarcsin(x)×(2/cbrt(x))

Derivada de y=lnarcsin(x)×(2/cbrt(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
               2  
log(asin(x))*-----
             3 ___
             \/ x
2x3log⁡(asin⁡(x))\frac{2}{\sqrt[3]{x}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} 
log(asin(x))*(2/x^(1/3))
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  2*log(asin(x))               2            
- -------------- + -------------------------
         4/3                ________        
      3*x          3 ___   /      2         
                   \/ x *\/  1 - x  *asin(x)
2x31−x2asin⁡(x)−2log⁡(asin⁡(x))3x43\frac{2}{\sqrt[3]{x} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{3 x^{\frac{4}{3}}}
Simplificar
Segunda derivada [src] 
  /     x                1                                                   \
  |----------- + -----------------                                           |
  |        3/2   /      2\                                                   |
  |/     2\      \-1 + x /*asin(x)                                           |
  |\1 - x /                          4*log(asin(x))              2           |
2*|------------------------------- + -------------- - -----------------------|
  |            asin(x)                       2               ________        |
  |                                       9*x               /      2         |
  \                                                   3*x*\/  1 - x  *asin(x)/
------------------------------------------------------------------------------
                                    3 ___                                     
                                    \/ x
2(x(1−x2)32+1(x2−1)asin⁡(x)asin⁡(x)−23x1−x2asin⁡(x)+4log⁡(asin⁡(x))9x2)x3\frac{2 \left(\frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}}{\operatorname{asin}{\left(x \right)}} - \frac{2}{3 x \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \frac{4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{9 x^{2}}\right)}{\sqrt[3]{x}}
Simplificar
Tercera derivada [src] 
  /                                            2                                                                                                       \
  |     1                 2                 3*x              3*x                                  x                1                                   |
  |----------- + -------------------- + ----------- - ------------------                     ----------- + -----------------                           |
  |        3/2           3/2                    5/2            2                                     3/2   /      2\                                   |
  |/     2\      /     2\        2      /     2\      /      2\                              /     2\      \-1 + x /*asin(x)                           |
  |\1 - x /      \1 - x /   *asin (x)   \1 - x /      \-1 + x / *asin(x)   28*log(asin(x))   \1 - x /                                     4            |
2*|--------------------------------------------------------------------- - --------------- - ------------------------------- + ------------------------|
  |                               asin(x)                                           3                   x*asin(x)                      ________        |
  |                                                                             27*x                                              2   /      2         |
  \                                                                                                                            3*x *\/  1 - x  *asin(x)/
--------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         3 ___                                                                          
                                                                         \/ x
2(3x2(1−x2)52−3x(x2−1)2asin⁡(x)+1(1−x2)32+2(1−x2)32asin⁡2(x)asin⁡(x)−x(1−x2)32+1(x2−1)asin⁡(x)xasin⁡(x)+43x21−x2asin⁡(x)−28log⁡(asin⁡(x))27x3)x3\frac{2 \left(\frac{\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{3 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}}}{\operatorname{asin}{\left(x \right)}} - \frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}}{x \operatorname{asin}{\left(x \right)}} + \frac{4}{3 x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - \frac{28 \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{27 x^{3}}\right)}{\sqrt[3]{x}}
Simplificar
Gráfico
Derivada de y=lnarcsin(x)×(2/cbrt(x))
    © Sr Examen – Калькулятор