Sr Examen

Derivada de y=ln(arcsin(5x))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
log(asin(5*x))
$$\log{\left(\operatorname{asin}{\left(5 x \right)} \right)}$$
log(asin(5*x))
Gráfica
Primera derivada [src]
           5            
------------------------
   ___________          
  /         2           
\/  1 - 25*x  *asin(5*x)
$$\frac{5}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}}$$
Segunda derivada [src]
   /          1                   5*x      \
25*|---------------------- + --------------|
   |/         2\                        3/2|
   |\-1 + 25*x /*asin(5*x)   /        2\   |
   \                         \1 - 25*x /   /
--------------------------------------------
                 asin(5*x)                  
$$\frac{25 \left(\frac{5 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(25 x^{2} - 1\right) \operatorname{asin}{\left(5 x \right)}}\right)}{\operatorname{asin}{\left(5 x \right)}}$$
Tercera derivada [src]
    /                                                     2                               \
    |      1                      2                   75*x                   15*x         |
125*|-------------- + ------------------------- + -------------- - -----------------------|
    |           3/2              3/2                         5/2               2          |
    |/        2\      /        2\        2        /        2\      /         2\           |
    \\1 - 25*x /      \1 - 25*x /   *asin (5*x)   \1 - 25*x /      \-1 + 25*x / *asin(5*x)/
-------------------------------------------------------------------------------------------
                                         asin(5*x)                                         
$$\frac{125 \left(\frac{75 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} - \frac{15 x}{\left(25 x^{2} - 1\right)^{2} \operatorname{asin}{\left(5 x \right)}} + \frac{1}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(5 x \right)}}\right)}{\operatorname{asin}{\left(5 x \right)}}$$
Gráfico
Derivada de y=ln(arcsin(5x))