By definition of derivative we know that derivative of a function at a given real number say c is given by :

f’(c) =

let Z =

If somehow we got a form similar to that of in definition of derivative we can write it in a simpler form.

∴ Z = {adding & subtracting af(a) in numerator}

⇒ Z = {using algebra of limits}

Using the definition of the derivative , we have –

⇒ Z =

∴ Z = f(a) – a f’(a)