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The derivative of the function/ tanh((a*x)/2)

Derivative of tanh((a*x)/2)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
    /a*x\
tanh|---|
    \ 2 /
$$\tanh{\left(\frac{a x}{2} \right)}$$ 
tanh((a*x)/2)
The first derivative [src] 
  /        2/a*x\\
a*|1 - tanh |---||
  \         \ 2 //
------------------
        2
$$\frac{a \left(1 - \tanh^{2}{\left(\frac{a x}{2} \right)}\right)}{2}$$
Simplify
The second derivative [src] 
 2 /         2/a*x\\     /a*x\
a *|-1 + tanh |---||*tanh|---|
   \          \ 2 //     \ 2 /
------------------------------
              2
$$\frac{a^{2} \left(\tanh^{2}{\left(\frac{a x}{2} \right)} - 1\right) \tanh{\left(\frac{a x}{2} \right)}}{2}$$
Simplify
The third derivative [src] 
  3 /         2/a*x\\ /           2/a*x\\ 
-a *|-1 + tanh |---||*|-1 + 3*tanh |---|| 
    \          \ 2 // \            \ 2 // 
------------------------------------------
                    4
$$- \frac{a^{3} \left(\tanh^{2}{\left(\frac{a x}{2} \right)} - 1\right) \left(3 \tanh^{2}{\left(\frac{a x}{2} \right)} - 1\right)}{4}$$
Simplify
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