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The derivative of the function/ acosh(t/a)

Derivative of acosh(t/a)

Function f() - derivative -N order at the point
v

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from to

Piecewise:

The solution

You have entered [src] 
     /t\
acosh|-|
     \a/
$$\operatorname{acosh}{\left(\frac{t}{a} \right)}$$ 
acosh(t/a)
The first derivative [src] 
        1        
-----------------
        _________
       /       2 
      /       t  
a*   /   -1 + -- 
    /          2 
  \/          a
$$\frac{1}{a \sqrt{-1 + \frac{t^{2}}{a^{2}}}}$$
Simplify
The second derivative [src] 
      -t       
---------------
            3/2
   /      2\   
 3 |     t |   
a *|-1 + --|   
   |      2|   
   \     a /
$$- \frac{t}{a^{3} \left(-1 + \frac{t^{2}}{a^{2}}\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
            2    
         3*t     
-1 + ------------
        /      2\
      2 |     t |
     a *|-1 + --|
        |      2|
        \     a /
-----------------
             3/2 
    /      2\    
  3 |     t |    
 a *|-1 + --|    
    |      2|    
    \     a /
$$\frac{-1 + \frac{3 t^{2}}{a^{2} \left(-1 + \frac{t^{2}}{a^{2}}\right)}}{a^{3} \left(-1 + \frac{t^{2}}{a^{2}}\right)^{\frac{3}{2}}}$$
Simplify
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