Find dy/dx

in terms of x

and y

if cos

2

(2y)+sin

2

(2y)=y+9

.

(1 point) Find dy/dx in terms of x and y if cos? (2y) + sin (2y) = y + 9. dy dx(1 point) Find the slope of the tangent line to the curve (a lemniscate) 2(x2 + y2) 2 = 25 (x2 - y2) at the point (-3, -1). m =(1 point) For the equation given below, evaluate y' at the point (1, 1). 3e\" 5x=y+2.15. y' at(1, 1): \f\f\f(1 point) Find dy/dx in terms of x and y if ax - by = c'. Assume that a, b and c are constants. dy dx\f\f(1 pt) The graph of the equation x? + ry ty? = 9 is a slanted ellipse illustrated in this figure: -2 -1 X N- Think of y as a function of T. Differentiating implicitly and solving for y' gives: -2- y= (Your answer will depend on T and y.) The ellipse has two horizontal tangents. The upper one has the equation y = The right most vertical tangent has the equation That tangent touches the ellipse where y = Hint: The horizontal tangent is of course characterized by y' = 0. To find the vertical tangent use symmetry, or think of I" as a function of y, differentiate implicitly, solve for ' and then set x' = 0