Derivative of tanh(ax)

You have entered [src]

tanh(a*x)

$$\tanh{\left(a x \right)}$$

d            
--(tanh(a*x))
dx

$$\frac{\partial}{\partial x} \tanh{\left(a x \right)}$$

Transform

The first derivative [src]

  /        2     \
a*\1 - tanh (a*x)/

$$a \left(1 - \tanh^{2}{\left(a x \right)}\right)$$

Simplify

The second derivative [src]

   2 /         2     \          
2*a *\-1 + tanh (a*x)/*tanh(a*x)

$$2 a^{2} \left(\tanh^{2}{\left(a x \right)} - 1\right) \tanh{\left(a x \right)}$$

Simplify

The third derivative [src]

    3 /         2     \ /           2     \
-2*a *\-1 + tanh (a*x)/*\-1 + 3*tanh (a*x)/

$$- 2 a^{3} \left(\tanh^{2}{\left(a x \right)} - 1\right) \left(3 \tanh^{2}{\left(a x \right)} - 1\right)$$

Simplify