Derivative of x squared is 2x or x ? Where is the fallacy? We all know that the derivative of $x^2$ is 2x. But what if someone proves it to be just x?

Solving Ramanujan’s Puzzling Problem Consider a sequence of functions as follows:- $ f_1 (x) = \sqrt {1+\sqrt {x} } $ $ f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } } $ $ f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } } $ ……and so on to $ f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt…