JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(y(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)\) Then \(y^{\prime}-y^{\prime \prime}\) at \(x=-1\) is equal to
- A \(976\)
- B \(464\)
- C \(496\)
- D \(944\)
Answer & Solution
Correct Answer
(C) \(496\)
Step-by-step Solution
Detailed explanation
\(y=\frac{1-x^{32}}{1-x} \Rightarrow y-x y=1-x^{32}\) \(y^{\prime}-x y^{\prime}-y=-32 x^{31}\) \(y^{\prime \prime}-x y^{\prime \prime}-y^{\prime}-y^{\prime}=-(32)(31) x^{30}\) \(\text { at } x=-1 \Rightarrow y^{\prime}-y^{\prime \prime}=496\)
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