Find the derivative of the following functions 'ab initio', that is, using the definition.
`s^2-bs+5`

Explanation

Let `y=s^2-bs+5`
Then
`(dy)/(ds)=lim_(hto0)((s+h)^2-b(s+h)+5-(s^2-bs-5))/h`
`=lim_(hto0)((s^2
+2hs+h^2-bs-bh+5-s^2+bs-5))/h`
`=lim_(hto0)(2hs-bh+h^2)/h`
`=lim_(hto0){2s-b+h}=2s-b`