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We know that d/dx(exp(cx))=c(exp(cx)), where c is a constant.
Does there exist a function g(cx) such that d/dx(exp(g(cx)))=1/c(exp(g(cx))) ?
Does there exist a function g(cx) such that d/dx(exp(g(cx)))=1/c(exp(g(cx))) ?
That doesn't really answer the question. All you have isIf cx=h, then g(h)=h/c^{2}.
de^{g(h)}/dx=(dg/dh)(dh/dx)e^{g(h)}=(1/c2)(c)e^{g(h)}=(1/c)e^{g(h)}