Sr Examen

Derivada de y=sin(x+3)-arcsin3x

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

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Solución

Ha introducido [src]
sin(x + 3) - asin(3*x)
$$\sin{\left(x + 3 \right)} - \operatorname{asin}{\left(3 x \right)}$$
sin(x + 3) - asin(3*x)
Gráfica
Primera derivada [src]
        3                   
- ------------- + cos(x + 3)
     __________             
    /        2              
  \/  1 - 9*x               
$$\cos{\left(x + 3 \right)} - \frac{3}{\sqrt{1 - 9 x^{2}}}$$
Segunda derivada [src]
 /     27*x                 \
-|------------- + sin(3 + x)|
 |          3/2             |
 |/       2\                |
 \\1 - 9*x /                /
$$- (\frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \sin{\left(x + 3 \right)})$$
Tercera derivada [src]
 /                         2                \
 |      27            729*x                 |
-|------------- + ------------- + cos(3 + x)|
 |          3/2             5/2             |
 |/       2\      /       2\                |
 \\1 - 9*x /      \1 - 9*x /                /
$$- (\frac{729 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \cos{\left(x + 3 \right)} + \frac{27}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}})$$
Gráfico
Derivada de y=sin(x+3)-arcsin3x