g(x) =e ^tgx

It seems you are defining a function \( g(x) = e^{t \cdot g(x)} \). However, the expression may involve some confusion with the variable \( t \).

Could you clarify if you meant \( g(x) = e^{t \cdot g(x)} \), and what is the variable \( t \)? Is \( t \) a constant or another function of \( x \)?

If you would like to solve the equation, find its derivative, or analyze it in any particular way, please provide more context or details (such as any particular values for \( t \) or what you want to find).