Sr Examen

Derivada de y=7sinα+4ctgα−2arccosα

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

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Solución

Ha introducido [src]
7*sin(a) + 4*cot(a) - 2*acos(a)
$$\left(7 \sin{\left(a \right)} + 4 \cot{\left(a \right)}\right) - 2 \operatorname{acos}{\left(a \right)}$$
7*sin(a) + 4*cot(a) - 2*acos(a)
Gráfica
Primera derivada [src]
          2           2                
-4 - 4*cot (a) + ----------- + 7*cos(a)
                    ________           
                   /      2            
                 \/  1 - a             
$$7 \cos{\left(a \right)} - 4 \cot^{2}{\left(a \right)} - 4 + \frac{2}{\sqrt{1 - a^{2}}}$$
Segunda derivada [src]
                2*a         /       2   \       
-7*sin(a) + ----------- + 8*\1 + cot (a)/*cot(a)
                    3/2                         
            /     2\                            
            \1 - a /                            
$$\frac{2 a}{\left(1 - a^{2}\right)^{\frac{3}{2}}} + 8 \left(\cot^{2}{\left(a \right)} + 1\right) \cot{\left(a \right)} - 7 \sin{\left(a \right)}$$
Tercera derivada [src]
                 2                                                              2   
    /       2   \                    2              2    /       2   \       6*a    
- 8*\1 + cot (a)/  - 7*cos(a) + ----------- - 16*cot (a)*\1 + cot (a)/ + -----------
                                        3/2                                      5/2
                                /     2\                                 /     2\   
                                \1 - a /                                 \1 - a /   
$$\frac{6 a^{2}}{\left(1 - a^{2}\right)^{\frac{5}{2}}} - 8 \left(\cot^{2}{\left(a \right)} + 1\right)^{2} - 16 \left(\cot^{2}{\left(a \right)} + 1\right) \cot^{2}{\left(a \right)} - 7 \cos{\left(a \right)} + \frac{2}{\left(1 - a^{2}\right)^{\frac{3}{2}}}$$
Gráfico
Derivada de y=7sinα+4ctgα−2arccosα