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No, its valid only when the domain of the functions are preserved during the transformation.
Lets consider an example X = a sin ωt and Y = b cos ωt then Z = dY/dX
= -b/a tan ωt, now the function Z is defined for all values of t except when t is 2nΠ ± Π/2 but the function M = dY/dt = -b sin ωt is defined for all values of t.
However we observe that M = Z . dX/dt = -b/a tan ωt * a cos ωt, would hold good if we can ensure that the domain of t is restricted to all real values except 2nΠ ± Π/2.
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