Here are five implicit differentiation problems, progressively ranging from easy to hard:

Easy:

1. Find $\frac{dy}{dx}$ for:
   $x^2 + y^2 = 25$

Medium:

2. Find $\frac{dy}{dx}$ for:
   $x^3 + y^3 = 6xy$

3. Find $\frac{dy}{dx}$ for:
   $x^2 + 2xy + y^2 = 10$

Hard:

4. Find $\frac{dy}{dx}$ for:
   $e^x + y^2 = xy$

5. Find $\frac{dy}{dx}$ for:
   $\sin(xy) = x + y$

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Would you like help with any of these, or do you want to try solving them first? Let me know if you have any questions!

Further Related Questions:

1. How do you handle implicit differentiation with logarithmic functions?
2. What is the chain rule, and how is it applied in implicit differentiation?
3. Can implicit differentiation be used to solve related rates problems?
4. How do you approach problems that involve products of variables (like $xy$) in implicit differentiation?
5. What are the common mistakes when differentiating implicitly, and how can you avoid them?

Tip: Always remember to differentiate both sides of the equation with respect to $x$, and apply the chain rule to terms involving $y$.