The central theme of the following assignments is to calculate the derivative of an implicitly defined function .

1. Calculate if:

2. Calculate if:

3. Calculate if:

4. Calculate if:

5. Calculate the tangent line at the point of the graph of the following expression:

6. Calculate the tangent line at the point of the graph of the following expression:

7. Calculate if:

8. If is a differentiable function of satisfying the following equation:

calculate .

9. Calculate the tangent line at the point of the graph of the following expression:

10. The equation:

defines as a differentiable function of close to the point .

Calculate the tangent line of the graph at this point.