Implicit differentiation
Grade 12 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Ari differentiates x² + y² = 25 implicitly. What is dy/dx at the point (3, 4)?
Bo differentiates x² + y² = 169 implicitly. What is dy/dx at the point (-5, 12)?
Esme differentiates x² + y² = 100 implicitly. What is dy/dx at the point (6, -8)?
Jun differentiates x² + y² = 289 implicitly. What is dy/dx at the point (8, 15)?
y is a function of x. Kira differentiates y³ with respect to x. Which is right?
- d/dx (y³) = 3x²
- d/dx (y³) = 3y² · dy/dx
- d/dx (y³) = 3y²
- d/dx (y³) = 3y² · dx/dy
y is a function of x. Milo differentiates eʸ with respect to x. Which is right?
- d/dx (eʸ) = eʸ · dy/dx
- d/dx (eʸ) = eʸ
- d/dx (eʸ) = eˣ
- d/dx (eʸ) = eʸ · dx/dy
y is a function of x. Noah differentiates ln y with respect to x. Which is right?
- d/dx (ln y) = (1/y) · dx/dy
- d/dx (ln y) = (1/y) · dy/dx
- d/dx (ln y) = 1/y
- d/dx (ln y) = 1/x
Pia differentiates xy = 12 implicitly with the product rule. What is dy/dx at (2, 6)?
Ren differentiates xy = -12 implicitly with the product rule. What is dy/dx at (3, -4)?
Zee differentiates xy = 8 implicitly with the product rule. What is dy/dx at (4, 2)?
