Sr Examen

Derivada de y=cos^-1x-xsech^-1x

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

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Solución

Ha introducido [src]
  1         x   
------ - -------
cos(x)   sech(x)
$$- \frac{x}{\operatorname{sech}{\left(x \right)}} + \frac{1}{\cos{\left(x \right)}}$$
1/cos(x) - x/sech(x)
Gráfica
Primera derivada [src]
     1       sin(x)   x*tanh(x)
- ------- + ------- - ---------
  sech(x)      2       sech(x) 
            cos (x)            
$$- \frac{x \tanh{\left(x \right)}}{\operatorname{sech}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{1}{\operatorname{sech}{\left(x \right)}}$$
Segunda derivada [src]
                          2        /         2   \         2   
  1      2*tanh(x)   2*sin (x)   x*\-1 + tanh (x)/   x*tanh (x)
------ - --------- + --------- + ----------------- - ----------
cos(x)    sech(x)        3            sech(x)         sech(x)  
                      cos (x)                                  
$$\frac{x \left(\tanh^{2}{\left(x \right)} - 1\right)}{\operatorname{sech}{\left(x \right)}} - \frac{x \tanh^{2}{\left(x \right)}}{\operatorname{sech}{\left(x \right)}} + \frac{2 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \tanh{\left(x \right)}}{\operatorname{sech}{\left(x \right)}} + \frac{1}{\cos{\left(x \right)}}$$
Gráfico
Derivada de y=cos^-1x-xsech^-1x