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Example 1: z=x³y_x=2t and y=t² Find dz dt

Example 1: z=x³y_x=2t and y=t² Find dz dt

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 5E
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Example 1:=x³y_x=2t and y=t² Find dz dt = Applications: 2.As a solid right circular cylinder is heated, its radius r and height h increase. So does surface area S. Suppose that at the instant when r =10cm and h = 100cm, r is increasing at 0.2 cm/h and h is increasing at 0.5cm/h. How fast is S increasing? 3.The temperature of a metal plate at (x,y) is ex-3y degrees. A bug is walking northeast in such a way that dx/dt =dy/dt =2. From the bugs point of view, how is the temperature changing with time as it crosses the origin ?
Transcribed Image Text:Example 1:=x³y_x=2t and y=t² Find dz dt = Applications: 2.As a solid right circular cylinder is heated, its radius r and height h increase. So does surface area S. Suppose that at the instant when r =10cm and h = 100cm, r is increasing at 0.2 cm/h and h is increasing at 0.5cm/h. How fast is S increasing? 3.The temperature of a metal plate at (x,y) is ex-3y degrees. A bug is walking northeast in such a way that dx/dt =dy/dt =2. From the bugs point of view, how is the temperature changing with time as it crosses the origin ?
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