AP EAMCET · Maths · Differentiation
If \(y=1+x+x^2+x^3+\ldots .+\infty\) and \(|x| \lt 1\), then \(y^{\prime \prime}=\)
- A \(2 y y^{\prime}\)
- B \(\frac{2 y}{y^{\prime}}\)
- C \(\frac{y^{\prime}}{2 y}\)
- D \(2 y^2 y^{\prime}\)
Answer & Solution
Correct Answer
(A) \(2 y y^{\prime}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y=1+x+x^2+x^3+\ldots+\infty \Rightarrow y=\frac{1}{1-x} \\ \therefore y^{\prime} & =\frac{1}{(1-x)^2} \Rightarrow y^{\prime \prime}=\frac{2}{(1-x)^3}=2 y y^{\prime}\end{aligned}\)
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