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xsinh^-1(x)-sqrtx²+1

Derivada de xsinh^-1(x)-sqrtx²+1

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

Ha introducido [src]
               2    
   x        ___     
------- - \/ x   + 1
sinh(x)             
$$\left(- \left(\sqrt{x}\right)^{2} + \frac{x}{\sinh{\left(x \right)}}\right) + 1$$
x/sinh(x) - (sqrt(x))^2 + 1
Gráfica
Primera derivada [src]
        1      x*cosh(x)
-1 + ------- - ---------
     sinh(x)        2   
                sinh (x)
$$- \frac{x \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)}} - 1 + \frac{1}{\sinh{\left(x \right)}}$$
Segunda derivada [src]
                         2   
     2*cosh(x)   2*x*cosh (x)
-x - --------- + ------------
      sinh(x)          2     
                   sinh (x)  
-----------------------------
           sinh(x)           
$$\frac{- x + \frac{2 x \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}} - \frac{2 \cosh{\left(x \right)}}{\sinh{\left(x \right)}}}{\sinh{\left(x \right)}}$$
Tercera derivada [src]
           2              3                 
     6*cosh (x)   6*x*cosh (x)   5*x*cosh(x)
-3 + ---------- - ------------ + -----------
          2             3          sinh(x)  
      sinh (x)      sinh (x)                
--------------------------------------------
                  sinh(x)                   
$$\frac{\frac{5 x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} - \frac{6 x \cosh^{3}{\left(x \right)}}{\sinh^{3}{\left(x \right)}} - 3 + \frac{6 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}}{\sinh{\left(x \right)}}$$
Gráfico
Derivada de xsinh^-1(x)-sqrtx²+1