Implicit Differentiation Practice

Implicit Differentiation Practice

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:

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).