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In Example 1.3.4 we arrived at a model for the length of daylight (in hours) in Philadelphia on the $ t $ th day of the year:$ L(t) = 12 + 2.8 \sin [ \frac {2 \pi}{365}(t - 80] $Use this model to compare how the number of hours of daylight is increasing in Philadelphia on March 21 and May 21.

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

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.

04:36

In Example 1.3.4 we arrive…

03:06

In Example 4 in Section 1.…

03:32

02:35

02:55

A model for the length of …

05:52

'model for the length…

02:26

03:31

In Example 1.3 .4 we arriv…

03:40

In Philadelphia the number…

07:19

Hours of Daylight In Phila…

06:46

The function $L(t)=12+5.5 …

So here we take it ho. The number of hours of daylight is increasing. So? So how much is increasing? We can take the derivative, and this one should be two point eight times to pie over his three sixty five co sign to pie over three sixty five T minus eighty. They just have to ah, clubbing those t value. So So for march twenty first, t should be generally has just thirty one days. February, assuming it's not a special years is twenty eight days and made twenty one. You have thirty one clause twenty, eh? Post large and April there are thirty days. So you just pulling these two t value kes into the original equation and you can use culturally threatened simplify that.

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