Find dy/da if 3x2y - 3y = 23 -4. Solve for y, then differentiate. dy dx See Example 1 page 131 for a similar example.Find dy/da if x2 + 2y = x+9. Do not solve for y first; instead, use implicit differentiation. Leave y in your answer. dy dx See Example 2 page 132 for a similar example.Find the equation of the tangent line to the curve y3 4my2 + cos 3mg = 2 at the point (0, 1). y 2 {3+ See Example 3 page 132 for a similar example. If y = 2m5/3 + (713241, find ny using the generalized power rule in Theorem A on page 133. See Example 4 page 133 for a similar example. Use implicit differentiation to find the slope of the tangent line to the curve 4m2 2mg 1y3 = 57 at the point (4, 1). m: 3/\" Find the equation of the tangent line to the curve (an ellipse) % + T = 1 at the point (3, ix/) The equation of this tangent line can be written in the form 3; = mm + b where m is: and where b is: A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 6 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 12 feet high? feet per second See Example 1 page 135 for a sketch and a similar example. Water is pouring into a conical tank at the rate of 8 cubic feet per minute. If the height of the tank is 12 feet and the radius of its circular opening is 3 feet how fast is the water level rising when the water is 4 feet deep? feet per minute See Example 2 page 136 for a sketch and a similar example. An airplane flying north at 480 miles per hour passes over a certain town at noon. A second airplane going east at 300 miles per hour is directly over the same town 15 minutes later. if the airplanes are flying at the same altitude, how fast will they be separating at 1 :15 RM? miles per hour See Example 3 page 138 for a sketch and a similar example. A woman standing on a cliff is watching a motorboat through a telescope as the boat approaches the shoreline directly below her. If the telescope is 100 feet above the water level and if the boat is approaching at 20 feet per seconds, at what rate is the angle of the telescope changing when the boat is 100 feet from the shore? negative radian per second See Example 4 page 139 for a sketch and a similar example