Derivative of Composition of Functions

Calculus Level 2

There is a certain function ff such that the tangent line at x=12x=\frac{1}{2} is y=2x+1.y=2x+1.

Given that g(x)=f(sinx),g(x)=f(\sin x), find the sum of all possible values of dgdx\frac{dg}{dx} when evaluated at x=π6x=\frac{\pi}{6}.

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