Sr Examen

Derivada de y=9sinα+2ctgα−7arccosα

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
9*sin(a) + 2*cot(a) - 7*acos(a)
$$\left(9 \sin{\left(a \right)} + 2 \cot{\left(a \right)}\right) - 7 \operatorname{acos}{\left(a \right)}$$
9*sin(a) + 2*cot(a) - 7*acos(a)
Gráfica
Primera derivada [src]
          2           7                
-2 - 2*cot (a) + ----------- + 9*cos(a)
                    ________           
                   /      2            
                 \/  1 - a             
$$9 \cos{\left(a \right)} - 2 \cot^{2}{\left(a \right)} - 2 + \frac{7}{\sqrt{1 - a^{2}}}$$
Segunda derivada [src]
              /       2   \              7*a    
-9*sin(a) + 4*\1 + cot (a)/*cot(a) + -----------
                                             3/2
                                     /     2\   
                                     \1 - a /   
$$\frac{7 a}{\left(1 - a^{2}\right)^{\frac{3}{2}}} + 4 \left(\cot^{2}{\left(a \right)} + 1\right) \cot{\left(a \right)} - 9 \sin{\left(a \right)}$$
Tercera derivada [src]
                           2                                                  2   
              /       2   \         7             2    /       2   \      21*a    
-9*cos(a) - 4*\1 + cot (a)/  + ----------- - 8*cot (a)*\1 + cot (a)/ + -----------
                                       3/2                                     5/2
                               /     2\                                /     2\   
                               \1 - a /                                \1 - a /   
$$\frac{21 a^{2}}{\left(1 - a^{2}\right)^{\frac{5}{2}}} - 4 \left(\cot^{2}{\left(a \right)} + 1\right)^{2} - 8 \left(\cot^{2}{\left(a \right)} + 1\right) \cot^{2}{\left(a \right)} - 9 \cos{\left(a \right)} + \frac{7}{\left(1 - a^{2}\right)^{\frac{3}{2}}}$$
Gráfico
Derivada de y=9sinα+2ctgα−7arccosα