If f(1) = 1, f’(1) = 2, then write the value of

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 =

As Z is taking 0/0 form because f(1) = 1

So on rationalizing the Z, we have–

Z =

⇒ Z = {using a²–b² = (a+b)(a–b)}

⇒ Z =

Using algebra of limits, we have –

Z =

Using the definition of the derivative, we have –

Z =

⇒ Z = 2 × (2/2) = 2 {using values given in equation}

∴ Z = 2