Implicit Differentiation Worksheet
A Grade 12 Calculus worksheet covering implicit differentiation with various question types.
Includes
Standards
Topics
Implicit Differentiation Practice
Name:
Date:
Score:
Read each question carefully and show all your work. Differentiate implicitly with respect to x.
1. Find dy/dx for the equation x² + y² = 25.
2. Find dy/dx for the equation y³ + x² = 4y.
3. If xy = 1, what is dy/dx?
1/x
-y/x
-1/x²
y/x
4. Which of the following equations requires implicit differentiation to find dy/dx?
y = x³ + 2x
y = sin(x)
x² + y² = 9
y = e^x
5. When differentiating implicitly, we treat y as a function of x, so we apply the rule when differentiating terms involving y.
6. The derivative of sin(y) with respect to x is .
7. Find dy/dx for the equation sin(y) + cos(x) = xy.
8. Find the equation of the tangent line to the curve x² + xy + y² = 7 at the point (1, 2).
9. Implicit differentiation is only used for equations that cannot be solved explicitly for y.
True
False