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Derivada de la función/ tg(x)/ arccos/ cos(x)/ y=tg(x)+cos(n*arccos(x))

Derivada de y=tg(x)+cos(n*arccos(x))

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

Ha introducido [src] 
tan(x) + cos(n*acos(x))
$$\cos{\left(n \operatorname{acos}{\left(x \right)} \right)} + \tan{\left(x \right)}$$ 
tan(x) + cos(n*acos(x))
Primera derivada [src] 
       2      n*sin(n*acos(x))
1 + tan (x) + ----------------
                   ________   
                  /      2    
                \/  1 - x
$$\frac{n \sin{\left(n \operatorname{acos}{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}} + \tan^{2}{\left(x \right)} + 1$$
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Segunda derivada [src] 
                          2                                    
  /       2   \          n *cos(n*acos(x))   n*x*sin(n*acos(x))
2*\1 + tan (x)/*tan(x) + ----------------- + ------------------
                                    2                   3/2    
                              -1 + x            /     2\       
                                                \1 - x /
$$\frac{n^{2} \cos{\left(n \operatorname{acos}{\left(x \right)} \right)}}{x^{2} - 1} + \frac{n x \sin{\left(n \operatorname{acos}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}$$
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Tercera derivada [src] 
               2                                                 3                       2                       2               
  /       2   \         2    /       2   \   n*sin(n*acos(x))   n *sin(n*acos(x))   3*x*n *cos(n*acos(x))   3*n*x *sin(n*acos(x))
2*\1 + tan (x)/  + 4*tan (x)*\1 + tan (x)/ + ---------------- - ----------------- - --------------------- + ---------------------
                                                       3/2                 3/2                     2                     5/2     
                                               /     2\            /     2\               /      2\              /     2\        
                                               \1 - x /            \1 - x /               \-1 + x /              \1 - x /
$$- \frac{n^{3} \sin{\left(n \operatorname{acos}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3 n^{2} x \cos{\left(n \operatorname{acos}{\left(x \right)} \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{3 n x^{2} \sin{\left(n \operatorname{acos}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{n \sin{\left(n \operatorname{acos}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}$$
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