Teaching UP TGT Mock Test Series 2025 Mathematics Differential Calculus Evaluation of derivatives

If \(y\, = \,1\, + \,\frac{1}{x} + \,\frac{1}{{{x^2}}} + \,\frac{1}{{{x^3}}} + \,...\)to ∞ with |x| > 1 then \(\frac{{dy}}{{dx}}\, =\)

1
\(\frac{{{x^2}}}{{{y^2}}}\)
2
x2y2
3
\(\frac{{{y^2}}}{{{x^2}}}\)
4
\(\frac{{{-y^2}}}{{{x^2}}}\)
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