Implicit Differentiation 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) Find the derivative given

(2) Find the derivative given

(3) Find the derivative given

(4) Find the derivative given

(5) Find the derivative given   

(6) Find the derivative given    

(7) Use implicit differentiation to find given

(8) Use implicit differentiation to find given   

(9) Use implicit differentiation to find given    

(10) Use implicit differentiation to find given     

(11) Use implicit differentiation to find given     

(12) Use implicit differentiation to find given     

(13) Use implicit differentiation to find and then find given

(14) Use implicit differentiation to find and then find given

(15) If find the value of at the point

(16) Verify that the point is on the curve and find equations for the lines that are tangent and normal to the curve at this point.

(17) Verify that the point is on the curve and find equations for the lines that are tangent and normal to the curve at this point.

(18) Verify that the point is on the curve and find equations for the lines that are tangent and normal to the curve at this point.

(19) Verify that the point is on the curve and find equations for the lines that are tangent and normal to the curve at this point.

(20) Find points on the curve (a) where the tangent is parallel to the -axis and (b) where the tangent is parallel to the -axis. In the latter case, is not defined, but is? What value does have at these points?

(21) The equations and define and implicitly as differentiable functions and find the slope of the curve at

(22) The equations and define and implicitly as differentiable functions and find the slope of the curve at

(23) Which of the following could be true if
    

(24) Use implicit differentiation to find   at for

(25) Use implicit differentiation to find   at for

(26) Use implicit differentiation to find   at for

(27) Use implicit differentiation to find   at for

(28) Use implicit differentiation to show that tangent line at to any ellipse centered at the origin has the form Also use implicit differentiation to show that tangent line at to any hyperbola centered at the origin has the form

(29) Show that the sum of the - and -intercepts of any tangent line to the curve is equal to

(30) Find the derivative of with respect to for the function .

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Implicit Differentiation Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/implicit-differentiation-homework.html