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A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei, for which the interval between times of maximum brightness is 5.4 days. The average brightness of this star is 4.0 and its brightness changes by $ \pm O.35. $ In view of these data, the brightness of Delta Cephei at time $ t, $ where $ t $ is measured in days, has been modeled by the function$ B(t) = 4.0 + 0.35 \sin (\frac {2 \pi t}{5.4}) $(a) Find the rate of change of the brightness after $ t $ days.(b) Find, correct to two decimal places, the rate of increase alter one day.

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00:51

Frank Lin

02:13

Heather Zimmers

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Francis E.

September 9, 2020

Campbell University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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A Cepheid variable star is…

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A variable star is one who…

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Delta Cephei is one of the…

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Variable Stars Variable st…

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the brightness of the star after two days is given as the A. T. 4.0 plus 0.357 to 5 to year over. 5.4. Give us information. We want to answer A and B. Find the rate of change and be after two days and be fined the rate of change of the after one day. As a note at the top indicates, this question is showing the understanding of different information using the channel. That is G. F. G. X. Dx is equal to F. Prime G of X. Where there were a half with G plugged in candy product. So to find the rate of change of B. After two days using the chamber, we have been trying to 40 or four plus 40.359 to 5 to 5.4 point 35 times signed. 2.25 point four G of X. Being to 5 to 5.4 G. Has delivered into five or 5.4. That's our Salvation 0.755 point 4% to 5 to 1.54 and B. We find the rate of change up to one day, such as two years and days. You simply plug in one. Thus, we find one is 10.75 or 5.4% to 5 times 1/5 50.4. Using a calculator, we obtain 0.16 per day for changing brightness per day.

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