Differential with a function of time

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safwatonline

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lets say z=dy/dx and m=dy/dt can i say that m=zdx/dt given that z is a function of time.
 

Re: differential

Hi,

You should consider practical examples to answer your question.
 

differential

well, the practical example is the original problem
 

Re: differential

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.

~Kalyan.
 

    safwatonline

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