Question

2. Find the following derivatives. 2s and zt, where z =9xy - 3x?y, x=2s+5t, and y = 2s - 5t dz gy6xy (Type an expression using x and y as the variables.) дх os = 2 (Type an expression using s and t as the variables.) dz = 9x - 3x2 (Type an expression using x and y as the variables.) dy = 2 (Type an expression using s and t as the variables.) dx = 5 (Type an expression using s and t as the variables.) dy = -5 (Type an expression using s and t as the variables.) Zs = (Type an expression using s and t as the variables.) Zt = (Type an expression using s and t as the variables.)

Answer 1

Given", = guy Buy: = 25+56 y = 23.56 We Knowi Z8 = 72 = 22 min + poza and Zx=82 = 87 on +27 ou le 11 : Since z = f(ny and a [ n, andy are functions of set Now; 82 y = ou ( gry - zuty) 9y – buy) { da cum) = com.emo y I on J ? cis constant. J Now, Similarly, 23 = 2 ay (any - Buty) 90 – 3427 oy = 0o (25-50) = 2 Again;

Boy - Box (28 +58) 3-5 Now substituting these values in ; = (9y-bay 2 + (gr - 342) = 184 122y + 185-642 1 Zs = 180 +184 - 12ny - Gul Similarly : = (99 - 6ry) 5 + ( 9u – 3x) <5) = 454-301y – 454 + 1542 = 1522 +459-454-3 ory .: 24 = 1522 +45g -454-3ony