Sr Examen

Derivada de y=arccosx*ctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
acos(x)*cot(x)
$$\cot{\left(x \right)} \operatorname{acos}{\left(x \right)}$$
acos(x)*cot(x)
Gráfica
Primera derivada [src]
/        2   \              cot(x)  
\-1 - cot (x)/*acos(x) - -----------
                            ________
                           /      2 
                         \/  1 - x  
$$\left(- \cot^{2}{\left(x \right)} - 1\right) \operatorname{acos}{\left(x \right)} - \frac{\cot{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
  /       2   \                                               
2*\1 + cot (x)/     x*cot(x)      /       2   \               
--------------- - ----------- + 2*\1 + cot (x)/*acos(x)*cot(x)
     ________             3/2                                 
    /      2      /     2\                                    
  \/  1 - x       \1 - x /                                    
$$- \frac{x \cot{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{acos}{\left(x \right)} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{\sqrt{1 - x^{2}}}$$
Tercera derivada [src]
/          2 \                                                                                              
|       3*x  |                                                                                              
|-1 + -------|*cot(x)                                                                                       
|           2|            /       2   \                                                        /       2   \
\     -1 + x /          6*\1 + cot (x)/*cot(x)     /       2   \ /         2   \           3*x*\1 + cot (x)/
--------------------- - ---------------------- - 2*\1 + cot (x)/*\1 + 3*cot (x)/*acos(x) + -----------------
             3/2                ________                                                              3/2   
     /     2\                  /      2                                                       /     2\      
     \1 - x /                \/  1 - x                                                        \1 - x /      
$$\frac{3 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) \operatorname{acos}{\left(x \right)} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \cot{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
Gráfico
Derivada de y=arccosx*ctgx