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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?

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

Derivatives

Differentiation

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### Video Transcript

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