Question

Given = xy -x^2y, x = s + t, y = s - t...Find Zs and Zt

Answer 1

Use chain rule\[\large
z_s = z_x\cdot x_s
\]

Answer 2

\[
z_x = y-2xy
\]\[
x_s = 1
\]\[
z_s = z_xx_s = y-2xy = (s-t)-2(s+t)(s-t) = s-t-2(s^2-t^2)
\]

Answer 3

Whoops... actually I should have put \[
z_s=z_xx_s+z_yy_s
\]

Answer 4

\[
z_y = x-x^2
\]

Answer 5

\[
y_s = 1
\]

Answer 6

so you have \[
z_s = (y+2xy) + (x-x^2)
\]

Answer 7

Please add a \Large command before every LaTeX line... the subscripts cannot be clearly seen without zooming the browser...