Evaluate: f(x)=ax+b

Expression: $f\left( x \right)=ax+b$

To find the derivative $f '\left( x \right)$ using the definition, evaluate the limit $\lim_{h \rightarrow 0} \left(\frac{ f\left( x+h \right)-f\left( x \right) }{ h }\right)$

$f '\left( x \right)=\lim_{h \rightarrow 0} \left(\frac{ a \times \left( x+h \right)+b-\left( ax+b \right) }{ h }\right)$

Evaluate the limit

$f '\left( x \right)=a$