Implicit Differentiation Practice
A Grade 9 math worksheet focusing on implicit differentiation with real problems and varied question types.
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Implicit Differentiation Practice
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Read each question carefully and show all your work. Remember to apply the chain rule when differentiating terms involving y.
1. Find dy/dx for the equation x² + y² = 25.
2. When implicitly differentiating an equation with respect to x, the derivative of a term like y³ is .
3. The chain rule states that d/dx [f(g(x))] = .
4. Which of the following equations requires implicit differentiation to find dy/dx?
y = x³ + 2x
y = sin(x)
x²y + y²x = 10
y = e^x
5. Implicit differentiation is used when y cannot be easily expressed as an explicit function of x.
True
False
6. Find the derivative dy/dx for the equation xy = 4.
7. Determine dy/dx for the equation sin(y) = x.