Explanation Given: The function of pulse rate of a runner is, P ( t ) = 300 1 2 t 2 + 2 t + 25 t + 25 Calculation: Section1: Differentiate the given function with respect to t , P ′ ( t ) = d d t [ 300 1 2 t 2 + 2 t + 25 t + 25 ] = 300 [ ( t + 25 ) d d t ( 1 2 t 2 + 2 t + 25 ) 1 2 − ( 1 2 t 2 + 2 t + 25 ) 1 2 d d t ( t + 25 ) ( t + 25 ) 2 ] = 300 [ ( t + 25 ) ( 1 2 ) ( ( 1 2 t 2 + 2 t + 25 ) − 1 2 ) ( t + 2 ) − ( 1 2 t 2 + 2 t + 25 ) 1 2 ( 1 ) ( t + 25 ) 2 ] = 300 [ ( t + 25 ) ( t + 2 ) 2 ( 1 2 t 2 + 2 t + 25 ) 1 2 − ( 1 2 t 2 + 2 t + 25 ) 1 2 ( t + 25 ) 2 ] Further solve the above equation P ′ ( t ) = 300 [ ( t + 25 ) ( t + 2 ) − 2 ( 1 2 t 2 + 2 t + 25 ) 2 ( t + 25 ) 2 1 2 t 2 + 2 t + 25 ] = 150 [ t 2 + 27 t + 50 − t 2 − 4 t − 50 ( t + 25 ) 2 1 2 t 2 + 2 t + 25 ] = 150 [ 23 t ( t + 25 ) 2 1 2 t 2 + 2 t + 25 ] = 3450 t ( t + 25 ) 2 1 2 t 2 + 2 t + 25 The derivative of the function of pulse rate P ( t ) = 300 1 2 t 2

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.3, Problem 77E

To determine

To find The derivative of given function of pulse rate, the rate at which the pulse rate is increases after 10 sec , 60 sec and 2 min after leaving the start line and the pulse rate 2 min into the run.

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Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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To find The derivative of given function of pulse rate, the rate at which the pulse rate is increases after 10 sec , 60 sec and 2 min after leaving the start line and the pulse rate 2 min into the run.

Solution Summary: The author calculates the derivative of the function of pulse rate of a runner with respect to t.

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To find The derivative of given function of pulse rate, the rate at which the pulse rate is increases after 10 sec , 60 sec and 2 min after leaving the start line and the pulse rate 2 min into the run.

Chapter 3 Solutions