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Mathematics Question on Derivatives

If y=log⁡x+log⁡x+log⁡x+log⁡x+.....+y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+}}}}.....+ then dydx\frac{dy}{dx} is :

A

1y(2x−1)\frac{1}{y(2x-1)}

B

1xy−1\frac{1}{xy-1}

C

1x(2y−1)\frac{1}{x(2y-1)}

D

1x(y−1)\frac{1}{x(y-1)}

Answer

1x(2y−1)\frac{1}{x(2y-1)}

Explanation

Solution

The correct option is (C) :1x(2y−1)\frac{1}{x(2y-1)}.