Chain Rules Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Write out the chain rule for the function where and

(2) Write out the chain rule for the function where and

(3) Find where and Leave your answer in mixed form

(4) Find where and Leave your answer in mixed form

(5) Find where and Leave your answer in mixed form

(6) Find where , and Leave your answer in mixed form

(7) Find and where , and Leave your answer in mixed form.

(8) Assuming the equation defines a differentiable function of , find

(9) Assuming the equation defines a differentiable function of , find

(10) Find the higher order partial derivatives and given the equation  

(11) Find the higher order partial derivatives and given the equation

(12) Find the higher order partial derivatives and given the equation

(13)  Use the chain rule for one parameter with

    (a) where and
    
    (b) where and

(14) Use the chain rule for two parameters with

    (a) where and
    
    (b) where and

(15) Let lie on the ellipsoid without solving for find and

(16) If show that

(17) If show that

(18) Let be a differentiable function of , where Show that

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Chain Rules Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/chain-rules-homework.html