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As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. When...

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As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. When the diameter is 30 cm at what rate is the area of the griddle changing?

A girl starts at a point A and runs east at a rate of 10 ft/sec. One minute later, another girl starts at A and runs north at a rate of 8 ft/sec. At what rate is the distance between them changing I minute after the second girl starts?

A metal rod has the shape of a right circular cylinder. As it is being heated, its length is increasing at a rate of 0.005 cm/min and its diameter is increasing at 0.002 cm/min. At what rate is the volume changing when the rod has length 40 cm and diameter 3 cm?

Product and Chain rule of differentiation

The chain rule is useful when the rate of change of one variable with respect to another is to be found out but is not directly available but is known indirectly through a third variable. The product rule is even more fundamental. It is used to find the derivative of a product of two or more number of variables. An example can be what is the rate of change of the area of a rectangle when we know the rate of change of length and breadth.

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{eq}\displaystyle \text { Let the diameter and area of the griddle be } D,A \text {respectively.} \\ \displaystyle \text {We are given }...

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Applying the Rules of Differentiation to Calculate Derivatives

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Chapter 8 / Lesson 13
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In this lesson, we'll review common derivatives and their rules, including the product, quotient and chain rules. We'll also examine how to solve derivative problems through several examples.


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