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  4. If y = x2 + (1/x2 (1)x2+(1)x2 +...∞, then (dy/dx) is

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Q. If $y = x^{2} + \frac{1}{x^{2} \frac{1}{x^{2}+\frac{1}{x^{2} +...\infty}}}$, then $\frac{dy}{dx}$ is

Limits and Derivatives

Solution:

$y = x^2 + \frac{1}{y}$
or $y^2 = x^2 y + 1$
or $2y \frac{dy}{dx} = y \cdot 2x + x^2 \frac{dy}{dx}$
or $\frac{dy}{dx} = \frac{2xy}{2y - x^2}$