help in find derivative of intervals function

Question

if the function is $f(x) = c + (x-a) (d-c) / (b-a)$ what the derivative is $f(x) ' =$?

I tried lookup for derivatives table, but find nothing meets my question.

Conditions are $a < b$, $c < d$, $a <= x <= b$.

Answer 1

$$f(x)=c+x.\frac{d-c}{b-a}-a\left(\frac{d-c}{b-a}\right)$$ $$\implies f'(x)= \frac{d-c}{b-a}$$