Differential with a function of time

[safwatonline]

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

 

[RFCMOS]

Re: differential

Hi,

You should consider practical examples to answer your question.

 

[safwatonline]

differential

well, the practical example is the original problem

 

[kalyanram]

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.

 

[Sayem Ahmed]

Re: differential

NICE EXAMPLE.