Question : 111) f(x, y) = (7x5y3 + 9)2 A) ∂f/∂x = 2(7x5y3 : 1757192

111) f(x, y) = (7x⁵y³ + 9)²

A) ∂f/∂x = 2(7x⁵y³ + 9); ∂f/∂y = 2(7x⁵y³ + 9)

B) ∂f/∂x = 42x⁵y²(7x⁵y³ + 9); ∂f/∂y = 70x⁴y³(7x⁵y³ + 9)

C) ∂f/∂x = 70x⁴y³(7x⁵y³ + 9); ∂f/∂y = 42x⁵y²(7x⁵y³ + 9)

D) ∂f/∂x = 35x⁴y³; ∂f/∂y = 21x⁵y²

112) f(x, y) =

113) f(x, y) =

114) f(x, y) = sin2 (-2xy² - y)

A) ∂f/∂x = 2sin (-2xy² - y) cos (-2xy² - y); ∂f/∂y = 2sin(-2xy² - y) cos(-2xy² - y)

B) ∂f/∂x = -4y²sin (-2xy² - y) cos (-2xy² - y); ∂f/∂y = 2sin (-2xy² - y) cos (-2xy² - y)

C) ∂f/∂x = 2sin (-2xy² - y) cos (-2xy² - y); ∂f/∂y = (-8x - 2) sin (-2xy² - y) cos (-2xy² - y)

D) ∂f/∂x = -4y²sin (-2xy² - y) cos (-2xy² - y); ∂f/∂y = (-8xy - 2) sin (-2xy² - y) cos (-2xy² - y)

115) f(x, y) = ln yx

A) ∂f/∂x = ln y; ∂f/∂y = x/y B) ∂f/∂x = xln y; ∂f/∂y = - x/y

C) ∂f/∂x = ln y; ∂f/∂y = - xln y D) ∂f/∂x = 0; ∂f/∂y = - x/y

116) f(x, y) = e-x/x² + y²

A) ∂f/∂x = e-x(x² + y² + 2x) / (x² + y²)2 ; ∂f/∂y = 2ye-x/ (x² + y²)2

B) ∂f/∂x = - 2xe-x/ (x² + y²)2 ; ∂f/∂y = - 2ye-x/ (x² + y²)2

C) ∂f/∂x = - e-x(x² + y² + x) / (x² + y²)2 ; ∂f/∂y = -ye-x/ (x² + y²)2

D) ∂f/∂x = -e-x(x² + y² + 2x) / (x² + y²)2 ; ∂f/∂y = -2ye-x/ (x² + y²)2

117) f(x, y) = x/x + y

118) f(x, y) = xye^-y

A) ∂f/∂x = ye-y; ∂f/∂y = - xye-y B) ∂f/∂x = ye-y; ∂f/∂y = xe-y(y - 1)

C) ∂f/∂x = ye-y; ∂f/∂y = xe-y(1 - y) D) ∂f/∂x = ye-y; ∂f/∂y = xe-y

119) f(x, y) = x³ + 7x²y + 9xy³

A) ∂f/∂x = 3x² + 2xy + 9y³; ∂f/∂y = 7x² + 3xy² B) ∂f∂x = 3x²; ∂f/∂y = 7x² + 27xy²

C) ∂f/∂x = x² + 7xy + 9y³; ∂f/∂y = 7x² + 9xy² D) ∂f/∂x = 3x² + 14xy + 9y³; ∂f/∂y = 7x² + 27xy²

120) f(x, y) = x² + y - ex⁺y