Implicit differentiation

Answer Key - Grade 12 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Ari differentiates x² + xy + y² = 7 implicitly. What is dy/dx at (1, 2)?

   -4/5
2. 2.

   Bo differentiates x² + xy + y² = 7 implicitly. What is dy/dx at (2, 1)?

   -5/4
3. 3.

   Esme differentiates x² + xy + y² = 7 implicitly. What is dy/dx at (-1, 3)?

   -1/5
4. 4.

   Kira finds the tangent line to x³ + y³ = 9 at (1, 2) and writes it as y = mx + b. What is b?

   9/4
5. 5.

   Luz finds the tangent line to x³ + y³ = 7 at (-1, 2) and writes it as y = mx + b. What is b?

   7/4
6. 6.

   Milo finds the tangent line to x³ + y³ = 28 at (1, 3) and writes it as y = mx + b. What is b?

   28/9
7. 7.

   Noah finds the tangent line to x³ + y³ = 35 at (2, 3) and writes it as y = mx + b. What is b?

   35/9
8. 8.

   Ren differentiates eʸ = x² implicitly and solves for dy/dx. Which is right?

   • dy/dx = −2x/eʸ
   • dy/dx = 2x/eˣ
   • dy/dx = 2x/eʸ
   • dy/dx = eʸ/(2x)
9. 9.

   Tala differentiates tan y = x implicitly and solves for dy/dx. Which is right?

   • dy/dx = cos² y
   • dy/dx = −cos² y
   • dy/dx = sec² y
   • dy/dx = cos² x
10. 10.

    Zee differentiates y + sin y = x implicitly and solves for dy/dx. Which is right?

    • dy/dx = 1 + cos y
    • dy/dx = −1/(1 + cos y)
    • dy/dx = 1/(1 + cos x)
    • dy/dx = 1/(1 + cos y)