1 Find and . f(x, y) = =- ; =- = ; = == ; = ; = 5 points QUESTION 2 Find the specific function value. Find f(3, 4) when f(x, y) = - . 5 points QUESTION 3 Find and . f(x, y) = = ; = = ; = - =- ; = = ; = 5 points QUESTION 4 Find the specific function value. Find f(0, 1, -1) when f(x, y, z) = 3x - 4yz + 9x. -3 -4 4 5 5 points QUESTION 5 Find fx, fy, and fz. f(x, y, z) = cos x sin2 (yz) fx = -sin x sin2 (yz); fy = 2z cos x sin (yz) cos (yz); fz = 2y cos x sin (yz) cos (yz) fx = sin x sin2 (yz); fy = -2z cos x sin (yz) cos (yz); fz = - 2y cos x sin (yz) cos (yz) fx = sin x sin2 (yz); fy = - cos x sin (yz) cos (yz); fz = -cos x sin (yz) cos (yz) fx = -sin x sin2 (yz); fy = z cos x sin (yz) cos (yz); fz = y cos x sin (yz) cos (yz) 5 points QUESTION 6 Find all the second order partial derivatives of the given function. f(x, y) = ex/y = ; = ex/y ; = = -ex/y = ; = ex/y ; = = -ex/y = ; = -ex/y ; = = ex/y = ; = ; = = 5 points QUESTION 7 Find and . f(x, y) = xye-y = ye-y; = xe- (y - 1) y = ye-y; = - xye-y = ye-y; = xe-y = ye-y; = xe- (1 - y) y 5 points QUESTION 8 Find fx, fy, and fz. f(x, y, z) = e(yz + sin x) fx = (cos x)e(yz + sin x); fy = ze(yz + sin x); fz = ye(yz + sin x) fx = (cos x + yz)e(yz + sin x); fy = ze(yz + sin ; fz = ye(yz + sin x) fx = (cos x)e(yz + sin x); fy = e(yz + sin x); fz = e(yz + sin x) fx = e(yz + sin x); fy = ze(yz + sin x); fz = ye(yz + sin x) x) 5 points QUESTION 9 Find f(x, y) = and . =- ; = =- ; = - = ; = =- ; = 5 points QUESTION 10 Find fx, fy, and fz. f(x, y, z) = fx = fx = fx = - ; fy = ; fy = ; fy = - ; fz = ; fz = ; fz = fx = ; fy = ; fz = 5 points QUESTION 11 Find all the second order partial derivatives of the given function. f(x, y) = ln (x2y - x) = ; =- ; = = ; = ; = =- ; = = - = ; = = = ; =- ; = = 5 points QUESTION 12 Find and f(x, y) = ln yx = ln y; = = ln y; = - xln y = xln y; =- . = 0; = 5 points QUESTION 13 Find and . f(x, y) = = ; =- = ; = = ; = - = ; = 5 points QUESTION 14 Find all the second order partial derivatives of the given function. f(x, y) = =- ; = ; = = =- ; = ; = = == ; = ; ; = =- = ; = = 5 points QUESTION 15 Find fx, fy, and fz. f(x,y,z) = xe(x2 + y2 + z2) fx = (1 + 2x2) e(x2 + y2 + z2); fy = xy2e(x2 + y2 + z2); fz = xz2e(x2 + y2 + z2) fx = 2x2e(x2 + y2 + z2); fy = xye(x2 + y2 + z2); fz = 2xze(x2 + y2 + z2) fx = (1 + 2x2) e(x2 + y2 + z2); fy = 2xye(x2 + y2 + z2); fz = 2xze(x 2 + y2 + z2) fx = (1 + 2x2) e(x2 + y2 + z2); fy = xe(x2 + y2 + z2); fz = xe(x2 + y2 + z2) 5 points QUESTION 16 Find and . f(x, y) = x3 + 9x2y + 2xy3 = 3x2 + 18xy + 2y3; = 9x2 + 6xy2 = x2 + 9xy + 2y3; = 9x2 + 2xy2 = 3x2; = 9x2 + 6xy2 = 3x2 + 2xy + 2y3; = 9x2 + 3xy2 5 points QUESTION 17 Find fx, fy, and fz. f(x, y, z) = fx = ; fy = - ; fz = fx = - ; fy = ; fz = fx = fx = - ; fy = ; fz = ; fy = - ; fz = 5 points QUESTION 18 Find the specific function value. Find f(3, 0, 9) when f(x, y, z) = 3x2 + 3y2 - z2. -72 -54 10 8 -48 5 points QUESTION 19 Find the specific function value. Find f(2, 3) when f(x, y) = (x + y)3. 15 25 12 5 35 5 points QUESTION 20 Find all the second order partial derivatives of the given function. f(x, y) = xye-y2 =0; = 2xye-y2(2y2 - 3); = = e- (1 - y2) y2 = ye-y2; = 2xye-y2(y2 - 1); = = e- (1 - y2) y2 = ye-y2; = 2xye-y2(2y2 - 6); = = e- (1 - 2y2) y2 = 0; (1 - 2y2) y2 = 2xye-y2(2y2 - 3); = = e- QUESTION 1 1. Find and . f(x, y) = =- =- =- = = - ; = - ; ; = - ; = 5 points QUESTION 2 1. Find the specific function value. Find f(3, 4) when f(x, y) = - . 5 points QUESTION 3 1. Find and . f(x, y) = = ; = = ; = - == ; ; = = 5 points QUESTION 4 1. Find the specific function value. Find f(0, 1, -1) when f(x, y, z) = 3x - 4yz + 9x. -3 -4 4 5 5 points QUESTION 5 1. Find fx, fy, and fz. f(x, y, z) = cos x sin2 (yz) fx = -sin x sin2 (yz); fy = 2z cos x sin (yz) cos (yz); fz = 2y cos x sin (yz) cos (yz) fx = sin x sin2 (yz); fy = -2z cos x sin (yz) cos (yz); fz = - 2y cos x sin (yz) cos (yz) fx = sin x sin2 (yz); fy = - cos x sin (yz) cos (yz); fz = -cos x sin (yz) cos (yz) fx = -sin x sin2 (yz); fy = z cos x sin (yz) cos (yz); fz = y cos x sin (yz) cos (yz) 5 points QUESTION 6 1. Find all the second order partial derivatives of the given function. f(x, y) = ex/y = ; = ex/y ; = = -ex/y = ; = ex/y ; = = -ex/y = ; = -ex/y ; = = ex/y = ; = ; = = 5 points QUESTION 7 1. Find and . f(x, y) = xye-y = ye-y; = xe-y(y - 1) = ye-y; = - xye-y = ye-y; = xe-y = ye-y; = xe-y(1 - y) 5 points QUESTION 8 1. Find fx, fy, and fz. f(x, y, z) = e(yz + sin x) fx = (cos x)e(yz + sin x); fy = ze(yz + sin x); fz = ye(yz + sin x) fx = (cos x + yz)e(yz + sin x); fy = ze(yz + sin x); fz = ye(yz + sin x) fx = (cos x)e(yz + sin x); fy = e(yz + sin x); fz = e(yz + sin x) fx = e(yz + sin x); fy = ze(yz + sin x); fz = ye(yz + sin x) 5 points QUESTION 9 1. Find and . f(x, y) = =- =- = =- = - ; ; = - = ; ; = 5 points QUESTION 10 1. Find fx, fy, and fz. f(x, y, z) = fx = ; fy = ; fz = fx = - ; fy = - fx = - ; fy = - fx = ; fz = - ; fy = ; fz = ; fz = 5 points QUESTION 11 1. Find all the second order partial derivatives of the given function. f(x, y) = ln (x2y - x) = ; =- = ; = = = =- ; ; =- = ; ; ; ; = - = = = = - = = 5 points QUESTION 12 1. Find and . f(x, y) = ln yx = ln y; = = ln y; = - xln y = xln y; = 0; == 5 points QUESTION 13 1. Find and . f(x, y) = = = ; =- ; = - = ; = - = ; = 5 points QUESTION 14 1. Find all the second order partial derivatives of the given function. f(x, y) = =- ; = ; = = =- ; = ; = = =- ; = ; = = = ; =- ; = = 5 points QUESTION 15 1. Find fx, fy, and fz. f(x,y,z) = xe(x2 + y2 + z2) fx = (1 + 2x2) e(x2 + y2 + z2); fy = xy2e(x2 + y2 + z2); fz = xz2e(x2 + y2 + z2) fx = 2x2e(x2 + y2 + z2); fy = xye(x2 + y2 + z2); fz = 2xze(x2 + y2 + z2) fx = (1 + 2x2) e(x2 + y2 + z2); fy = 2xye(x2 + y2 + z2); fz = 2xze(x2 + y2 + z2) fx = (1 + 2x2) e(x2 + y2 + z2); fy = xe(x2 + y2 + z2); fz = xe(x2 + y2 + z2) 5 points QUESTION 16 1. Find and . f(x, y) = x3 + 9x2y + 2xy3 = 3x2 + 18xy + 2y3; = x2 + 9xy + 2y3; = 3x2; = 9x2 + 6xy2 = 9x2 + 2xy2 = 9x2 + 6xy2 = 3x2 + 2xy + 2y3; = 9x2 + 3xy2 5 points QUESTION 17 1. Find fx, fy, and fz. f(x, y, z) = fx = fx = fx = ; fy = ; fy = ; fy = ; fz = ; fz = ; fz = fx = - ; fy = - ; fz = 5 points QUESTION 18 1. Find the specific function value. Find f(3, 0, 9) when f(x, y, z) = 3x2 + 3y2 - z2. -72 -54 108 -48 5 points QUESTION 19 1. Find the specific function value. Find f(2, 3) when f(x, y) = (x + y)3. 15 25 125 35 5 points QUESTION 20 1. Find all the second order partial derivatives of the given function. f(x, y) = xye-y2 =0; = 2xye-y2(2y2 - 3); = ye-y2; = 2xye-y2(y2 - 1); = ye-y2; = 2xye-y2(2y2 - 6); = 0; = 2xye-y2(2y2 - 3); = e-y2(1 - y2) = = = = = e-y2(1 - y2) = e-y2(1 - 2y2) = e-y2(1 - 2y2)