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The minute hand on a watch is $ 8 mm $ long and the hour hand is $ 4 mm $ long. How fast is the distance between the tips of the hands changing at one o'clock?

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$-18.6 \mathrm{mm} / \mathrm{hr}$

04:07

Wen Zheng

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Missouri State University

Campbell University

University of Nottingham

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.

16:33

The minute hand on a watch…

01:59

On a certain clock the min…

04:12

08:45

The hands on a clock are o…

02:26

The minute hand of a clock…

02:06

01:10

The hour and minute hands …

02:34

The minute hand and the ho…

Okay. We know that we can use the rule. Ax squared is force word plus eight squared minus two times four times 8% data the law of Co sign which we established. Therefore we know differentiating this. We have DX over DX DJ equals two times. Death it over. DT, which gives us t ax over. DT is 30 to sign data over Axe. Do you think it over g t? Because the Jews cancel like that. Okay, now that we have this, we know you can plug in. Max is squirt of four square plus eight squared minus two times four times a day. Co sign cry over sex, which gives us X is four squirt of five minus to squirt of three. Remember of the fact that detailed over DT is two pi over 12 minus two pi, which is negative. 11 pi over sex. So now we have 32 comes 1/2 over what we found earlier, which is for a squirt of five minutes to squirt of three comes negative 11 pie over sex, which gives this negative 18.6

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