121616949-math.102 - 88 Chapter 4 Transcendental Functions...

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88 Chapter 4 Transcendental Functions Exercises In exercises 1–8, find a formula for the derivative y at the point ( x, y ): 1. y 2 = 1 + x 2 2. x 2 + xy + y 2 = 7 3. x 3 + xy 2 = y 3 + yx 2 4. 4 cos x sin y = 1 5. x + y = 9 6. tan( x/y ) = x + y 7. sin( x + y ) = xy 8. 1 x + 1 y = 7 9. A hyperbola passing through (8 , 6) consists of all points whose distance from the origin is a constant more than its distance from the point (5,2). Find the slope of the tangent line to the hyperbola at (8 , 6). 10. Compute y for the ellipse of example 4.18 . 11. The graph of the equation x 2 - xy + y 2 = 9 is an ellipse. Find the lines tangent to this curve at the two points where it intersects the x -axis. Show that these lines are parallel. 12. Repeat the previous problem for the points at which the ellipse intersects the y -axis. 13. Find the points on the ellipse from the previous two problems where the slope is horizontal and where it is vertical. 14. Find an equation for the tangent line to x 4 = y 2 + x 2 at (2 , 12). (This curve is the
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