Implicit differentiation

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari differentiates x² + y² = 25 implicitly. What is dy/dx at the point (3, 4)?

   -3/4
2. 2.

   Bo differentiates x² + y² = 169 implicitly. What is dy/dx at the point (-5, 12)?

   5/12
3. 3.

   Esme differentiates x² + y² = 100 implicitly. What is dy/dx at the point (6, -8)?

   3/4
4. 4.

   Jun differentiates x² + y² = 289 implicitly. What is dy/dx at the point (8, 15)?

   -8/15
5. 5.

   y is a function of x. Kira differentiates y³ with respect to x. Which is right?

   • d/dx (y³) = 3y² · dx/dy
   • d/dx (y³) = 3x²
   • d/dx (y³) = 3y² · dy/dx
   • d/dx (y³) = 3y²
6. 6.

   y is a function of x. Noah differentiates ln y with respect to x. Which is right?

   • d/dx (ln y) = 1/x
   • d/dx (ln y) = (1/y) · dy/dx
   • d/dx (ln y) = 1/y
   • d/dx (ln y) = (1/y) · dx/dy
7. 7.

   Pia differentiates xy = 12 implicitly with the product rule. What is dy/dx at (2, 6)?

   -3
8. 8.

   Ren differentiates xy = -12 implicitly with the product rule. What is dy/dx at (3, -4)?

   4/3
9. 9.

   Tala differentiates xy = 10 implicitly with the product rule. What is dy/dx at (-2, -5)?

   -5/2
10. 10.

    Zee differentiates xy = 8 implicitly with the product rule. What is dy/dx at (4, 2)?

    -1/2