Problem:
Plot the graph of the relation

sin(x + y) = y2 cos(x)

and calculate the derivatve.


Visualization: Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph F(x,y)=c, press and .
  3. At the prompt F(x,y) =, enter the formula
    sin(x+y) - y^2 cos(x)
  4. and use the bounds
    x0 = -4 x1 = 4
    y0 = -3 y1 = 3
  5. At the prompt, N = , enter 1 and
  6. at the prompt, c_1 = , enter 0 You will then see the graph of this relation.

  7. Press and
  8. Use the arrow keys to move to Implicit Differ.and press and .
  9. Use the arrow keys to move to F(x,y)=0 and press .
  10. At the prompt F(x,y)= just press (the equation is still stored in the computer - just beneath the latter prompt you should see F(x,y) = Sin[x + y] - (y^2) Cos x).
  11. After a little delay, you should see:
       dy     dR/dx
       -- = - ----- ,  where
       dx     dR/dy
    
       dR/dx = Cos [x + y] + (y ^2) Sin x
    
       dR/dy = Cos [x + y] - 2(Cos x) y
    
       Press <Space>: