1. Warm up Problems 1. 2. 3.

3. Implicit Differentiation Ex. So far, all problems have been y = f (x)  What if x’s and y’s are mixed together?

4. Ex. If cos x + y 2 – y = x, find. Steps for Implicit Differentiation Derivative of x-function is the same as usual. Derivative of y-function gets. If x’s and y’s mixed, use product rule. Solve for.

5. Ex. If cos x + y 2 – y = x, find.

6. Ex.

7. Pract.

8. Ex. Find the slope of the line tangent to y = x + cos(xy) at the point where x = 0.

9. Ex. If cos x + y 2 – y = x, find.

10. Ex. Find the coordinates of any point on x 2 + y 2 = 16 where the tangent line has the slope of -1.

11. Ex. Let f (x) = x 3 + x. If g(x) = f -1 (x) and g(10) = 2, find g(10).

12. Next class, you will be taking a Derivative Quiz