M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 18/11/1441 AH, 6:03 PM Current Score QUESTION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 POINTS –/2 –/2 –/2 –/2 –/2 –/2 –/2 –/3 –/3 –/3 –/1 –/3 –/2 –/4 –/4 –/2 –/1 –/1 –/1 TOTAL SCORE –/42 0.0% Due Date FRI, JUL 10, 2020 11:55 PM EDT Request Extension Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 2 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 1. [–/2 Points] DETAILS SCALCET8 14.3.012. MY NOTES ASK YOUR TEACHER 18/11/1441 AH, 6:03 PM PRACTICE ANOTHER Find fx(1, 0) and fy(1, 0) and interpret these numbers as slopes for the following equation. f(x, y) = 4 − x2 − 5y2 fx(1, 0) = fy(1, 0) = 2. [–/2 Points] DETAILS SCALCET8 14.3.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the first partial derivatives of the function. f(x, y) = x6 + 8xy3 fx(x, y) = fy(x, y) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 3 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 3. [–/2 Points] DETAILS SCALCET8 14.3.017. MY NOTES 18/11/1441 AH, 6:03 PM ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER Find the first partial derivatives of the function. f(x, t) = t4e−x fx(x, t) = ft(x, t) = 4. [–/2 Points] DETAILS SCALCET8 14.3.020. Find the first partial derivatives of the function. z = x sin(xy) ∂z = ∂x ∂z = ∂y 5. [–/2 Points] DETAILS SCALCET8 14.3.021. Find the first partial derivatives of the function. f(x, y) = x y fx(x, y) = fy(x, y) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 4 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 6. [–/2 Points] DETAILS SCALCET8 14.3.024. 18/11/1441 AH, 6:03 PM MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the first partial derivatives of the function. w= ev u + v8 ∂w = ∂u ∂w = ∂v 7. [–/2 Points] DETAILS SCALCET8 14.3.028. Find the first partial derivatives of the function. f(x, y) = x6y fx(x, y) = fy(x, y) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 5 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 8. [–/3 Points] DETAILS SCALCET8 14.3.031. 18/11/1441 AH, 6:03 PM MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the first partial derivatives of the function. f(x, y, z) = x7yz2 + 6yz fx(x, y, z) = fy(x, y, z) = fz(x, y, z) = 9. [–/3 Points] DETAILS SCALCET8 14.3.033. Find the first partial derivatives of the function. w = ln(x + 4y + 3z) ∂w = ∂x ∂w = ∂y ∂w = ∂z https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 6 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 10. [–/3 Points] MY NOTES DETAILS 18/11/1441 AH, 6:03 PM SCALCET8 14.3.509.XP. ASK YOUR TEACHER PRACTICE ANOTHER Find the first partial derivatives of the function. w = 3zexyz ∂w = ∂x ∂w = ∂y ∂w = ∂z 11. [–/1 Points] MY NOTES DETAILS SCALCET8 14.3.513.XP. ASK YOUR TEACHER PRACTICE ANOTHER Find the indicated partial derivatives. f(x, y, z) = y ; x+y+z fy(2, −7, 8) fy(2, −7, 8) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 7 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 12. [–/3 Points] MY NOTES DETAILS SCALCET8 14.3.AE.004. ASK YOUR TEACHER Video Example 18/11/1441 AH, 6:03 PM PRACTICE ANOTHER Find ∂z/∂x and ∂z/∂y if z is defined implicitly as a function EXAMPLE 4 of x and y by the equation x4 + y4 + z4 + 8xyz = 1. SOLUTION To find ∂z/∂x, we differentiate implicitly with respect to x, being careful to treat y as a constant: ∂z + 8yz + 8xy ∂z = 0. ∂x ∂x Solving this equation for ∂z/∂x, we obtain + 4z3 ∂z = ∂x . Similarly, implicitly differentiating with respect to y gives ∂z = ∂y . 13. [–/2 Points] DETAILS SCALCET8 14.3.047. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use implicit differentiation to find ∂z/∂x and ∂z/∂y. x2 + 8y2 + 5z2 = 3 ∂z = ∂x ∂z = ∂y https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 8 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 14. [–/4 Points] MY NOTES DETAILS 18/11/1441 AH, 6:03 PM SCALCET8 14.3.515.XP. ASK YOUR TEACHER PRACTICE ANOTHER Find all the second partial derivatives. f(x, y) = x6y8 + 6x6y fxx(x, y) = fxy(x, y) = fyx(x, y) = fyy(x, y) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 9 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 15. [–/4 Points] DETAILS SCALCET8 14.3.518.XP.MI. 18/11/1441 AH, 6:03 PM MY NOTES ASK YOUR TEACHER ASK YOUR TEACHER PRACTICE ANOTHER Find all the second partial derivatives. v= xy x−y vxx = vxy = vyx = vyy = 16. [–/2 Points] DETAILS SCALCET8 14.3.063. MY NOTES Find the indicated partial derivative(s). f(x, y) = x6y4 − x5y3; fxxx, fxyx fxxx(x, y) = fxyx(x, y) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 10 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign 17. [–/1 Points] SCALCET8 14.3.522.XP. DETAILS 18/11/1441 AH, 6:03 PM MY NOTES ASK YOUR TEACHER ASK YOUR TEACHER PRACTICE ANOTHER ASK YOUR TEACHER PRACTICE ANOTHER Find the indicated partial derivative. z=u v − w; ∂3z = ∂u ∂v ∂w 18. [–/1 Points] ∂3z ∂u ∂v ∂w SCALCET8 14.4.001. DETAILS MY NOTES Find an equation of the tangent plane to the given surface at the specified point. z = 4x2 + y2 − 7y, 19. [–/1 Points] (1, 3, −8) DETAILS SCALCET8 14.4.006. MY NOTES Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 6y), (7, 1, 0) Submit Assignment Home Save Assignment Progress My Assignments https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Request Extension Page 11 of 12 M221_Sum Homework Assignment 7 (14.3, 14.4) - Math 221, section 25, Summer 2 2020 | WebAssign Copyright 18/11/1441 AH, 6:03 PM 2020 Cengage Learning, Inc. All Rights Reserved https://www.webassign.net/web/Student/Assignment-Responses/last?dep=23794431 Page 12 of 12
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