Sr Examen

Derivada de y=7sinα+5ctgα−7arccosα:

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

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Solución

Ha introducido [src]
7*sin(a) + 5*cot(a) - 7*acos(a)
$$\left(7 \sin{\left(a \right)} + 5 \cot{\left(a \right)}\right) - 7 \operatorname{acos}{\left(a \right)}$$
7*sin(a) + 5*cot(a) - 7*acos(a)
Gráfica
Primera derivada [src]
          2           7                
-5 - 5*cot (a) + ----------- + 7*cos(a)
                    ________           
                   /      2            
                 \/  1 - a             
$$7 \cos{\left(a \right)} - 5 \cot^{2}{\left(a \right)} - 5 + \frac{7}{\sqrt{1 - a^{2}}}$$
Segunda derivada [src]
                7*a          /       2   \       
-7*sin(a) + ----------- + 10*\1 + cot (a)/*cot(a)
                    3/2                          
            /     2\                             
            \1 - a /                             
$$\frac{7 a}{\left(1 - a^{2}\right)^{\frac{3}{2}}} + 10 \left(\cot^{2}{\left(a \right)} + 1\right) \cot{\left(a \right)} - 7 \sin{\left(a \right)}$$
Tercera derivada [src]
                  2                                                              2   
     /       2   \                    7              2    /       2   \      21*a    
- 10*\1 + cot (a)/  - 7*cos(a) + ----------- - 20*cot (a)*\1 + cot (a)/ + -----------
                                         3/2                                      5/2
                                 /     2\                                 /     2\   
                                 \1 - a /                                 \1 - a /   
$$\frac{21 a^{2}}{\left(1 - a^{2}\right)^{\frac{5}{2}}} - 10 \left(\cot^{2}{\left(a \right)} + 1\right)^{2} - 20 \left(\cot^{2}{\left(a \right)} + 1\right) \cot^{2}{\left(a \right)} - 7 \cos{\left(a \right)} + \frac{7}{\left(1 - a^{2}\right)^{\frac{3}{2}}}$$
Gráfico
Derivada de y=7sinα+5ctgα−7arccosα: