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

3. Ex. If , find

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

5. Ex. If , find

6. Ex. Find the coordinates of any point on
x2 + y2 = 16 where the tangent line has the slope of -1.

7. Ex. Let f (x) = x3 + x. If g(x) = f -1(x), find g(10).