DSolve::der1
NDSolve::der1
NDSolveValue::der1
ParametricNDSolve::der1
ParametricNDSolveValue::der1
An error occurs because Derivative[1][f, g][x] shows differentiation of both f and g:
NDSolve[{Derivative[1][f, g][x] == f[x], g'[x] == g[x], f[0] == g[0] == 1}, {f, g}, {x, 0, 1}]This shows a valid input to NDSolve:
NDSolve[{Derivative[1][f][x] == f[x], g'[x] == g[x], f[0] == g[0] == 1}, {f, g}, {x, 0, 1}]