Grings - Taxas Relacionadas Aula 1

Subscribe to my CHANNEL to receive FREE lessons WEBSITE: http://www.omatematico.com/ Lessons on DVD: http://www.lojaomatematico.com.br/ STUDYING has never been easier! CONTENT: 3 Exercises on Applications of Derivatives with Related Rates Introduction to Related Rates - Derivatives Review: Example: Given the function y = x², calculate dy/dx = ? Example: 4y³ = x² + 1, calculate dy/dx = ? in time (1:44) Exercise: y³ = x² + y + 2x³ + 3, calculate dy/dx = ? in time (4:03) Exercise: Derivative with respect to x y³ + 1 + z² = x² in time (6:34) Exercise: Derivative with respect to z y³ + 1 + z² = x² in time (8:17) Exercise: Derivative with respect to y y³ + 1 + z² = x² in time (9:51) Derivative of 1, which is a constant, is zero 1st property of the table in time (9:58) Derivative Table: http://bit.ly/1MZzwEg Exercise: Derivative with respect to t (although the variable t is not in the equation) y³ + 1 + z² = x² in time (10:44) Exercise 1: The volume of The spherical balloon shown in the figure grows at a rate of 100 cm³/s. What is the growth rate of the radius when it measures 50 cm? At time (12:15) dv/dt = 100 cm³/s dR/dt = ? OUTLINE to follow to solve the exercises At time (13:37) Step 1) Identify the variables Step 2) Find a relationship between the variables Step 3) Derivative with respect to the reference variable Step 4) Substitute the known values Step 5) Isolate what you want to calculate Exercise 2: An oil slick expands in a circular shape where the area grows at a constant rate of 26 km²/h. How fast will the slick's radius be changing when the area is 9 km²? in time (18:31) Exercise 3: A rocket ascends vertically and is accompanied by a ground station 5 km from the launch pad. How fast will the rocket be ascending when its altitude is 4 km and its distance from the station is increasing at 2,000 km/h? in time (26:00)