Question

If y = (1 + x)(1 + x²) ..... (1 + x¹⁰⁰) then \(\dfrac{dy}{dx}\) at x = 0 is
1. 100
2. 0
3. 1
4. 5050

Answer 1

Correct Answer - Option 3 : 1

y = (1 + x) (1 + x²) … (1 + x¹⁰⁰)

= (1 + x + x² + x³) … (1 + x¹⁰⁰)

As, we need to find the value of derivative with respect to x. 

At x = 0, we do not need to expand/simplify 'y' 

We only need x¹ term as all other terms in the expression of \(\left( {\frac{{dy}}{{dx}}} \right)\) will have ‘x’ term in them and hence becomes ‘0’ at x = 0

∴ \({\left. {\frac{{dy}}{{dx}}} \right|_{x = 0}} = 0 + 1 + 0 + 0 + \ldots \)

= 1