Implicit Differentiation Practice
A Grade 11 Calculus worksheet on implicit differentiation, covering finding derivatives of implicitly defined functions.
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Implicit Differentiation Practice
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Carefully read each question and show all your work. Find the derivative dy/dx for each implicitly defined function.
1. Find dy/dx for the equation: x² + y² = 25
2. Determine dy/dx given the equation: xy + y³ = 10
3. Find dy/dx for the equation: sin(y) + cos(x) = 1
4. If x² - y² = 1, then dy/dx is:
x/y
y/x
-x/y
-y/x
5. When differentiating implicitly, we treat y as a function of x, applying the rule whenever we differentiate a term involving y.
6. The derivative of ln(y) with respect to x is .
7. Find the equation of the tangent line to the curve x² + y² = 10 at the point (1, 3).
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