(related to Corollary: Derivative of a Linear Function \(ax+b\))
To calculate the derivative of a linear function \(f(x)=ax +b\), \(a,b\in\mathbb R\) we can apply the basic arithmetic operations involving derivatives and conclude
\[f'(x)=(ax +b)'=(ax)' +(b)'=a+0=a.\]
Herein, we have applied the rule \((1)\), the rule \((3)\), and the rule of a derivative of a constant function.
