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And this question we're asked that, given the rate
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of change of the length and the width of a
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rectangle, we want to find the length and the
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width of the, We want to find the rate
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of change of the area at a certain length and
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a certain width. Let's remember the formula for the
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area of a rectangle. We know that the area
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is equal to the length times the width, but
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All three of these are functions of time, so
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it's more correct to say that as a function of
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time, the area is, the length is a
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function of time, multiplied by the width times a
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function of time. Okay people, now that we
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have this information, we can go ahead and straight
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up, apply implicit differentiation and differentiate both sides with
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respect to time. Now the derivative of the area
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with respect to time is the rate of change of
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the area. And we know that that's going to
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be equal to the right hand side, which we're
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going to have to use the product rule which states
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to keep the first function and take the derivative of
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the second function and add it with the second function
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times the derivative of the first function. Now we
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know that were given to fixed lengths and width.
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That's these two numbers here. So let's plug these
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in. We know that the length is 20 And
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the width is 10. Yeah. And we're going
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to multiply that by the rate of change of the
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length and the rate of change of the width,
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Which is going to be three times eight. And
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when we add and when we simplify this together,
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we're going to get 60 plus 80 which is equal
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to 1 40 centimetres squared her second. And that's
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the answer to this question.