Chain Rule: Quantity raised to a power

Chain Rule: Quantity raised to a power

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The Chain Rule can be applied to find the derivative of a function such as

That is because this function can be considered (from the outside working in) as a quantity raised to the 8^th power. Frequently, it helps to temporarily define a variable, u, to represent the quantity.

Then

Here,

Then the function can be written as

, and the task of finding its derivative with respect to x becomes

The first stage, finding can be handled with the Power Rule:

In order to go further, we need to replace u with its equivalent:

We can use the Sum, Scalar Multiple, and Power Rules to complete the problem by differentiating the remaining terms to get

Test Problem: Find the derivative of

a)
b)
c)
d)

General Contents

Detailed Contents

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