- #1

TylerH

- 729

- 0

[tex]\mbox{Let }z=T(t)X(x)Y(y)[/tex]

[tex]T'(t)X(x)Y(y)=T(t)X'(x)Y(y)+T(t)X(x)Y'(y) \Rightarrow[/tex]

[tex]\frac{T'(t)}{T(t)}=\frac{X'(x)}{X(x)}+\frac{Y'(y)}{Y(y)} \Rightarrow[/tex]

[tex]\frac{T'(t)}{T(t)}=A \wedge \left(\frac{X'(x)}{X(x)}+\frac{Y'(y)}{Y(y)}=B \rightarrow \frac{X'(x)}{X(x)}=C \wedge \frac{Y'(y)}{Y(y)}=D \right)[/tex]

... and so on.