If z fxstyst exy tan y with xst s 2t and yst st you nee

If z = f(x(s,t),y(s,t)) = exy tan y with x(s,t) = s + 2t and y(s,t) = s/t, you need chain rule formulations to compute delta z/delta s and delta z/delta t.

Solution

\\(\\delta z/\\delta s = ye^{xy}\\tan y \\delta (s+2t)/\\delta s + (xe^{xy}\\tan y + e^{xy}\\sec^2 y)\\delta (s/t)/\\delta s\\) and \\(\\delta z/\\delta t = ye^{xy}\\tan y \\delta (s+2t)/\\delta t + (xe^{xy}\\tan y + e^{xy}\\sec^2 y)\\delta (s/t)/\\delta t\\)