The Chain Rule: Examples

1. Find $\frac{dw}{dt}$ when $dw$ is as follows:
 MATH

Answer:

To find this, we must use the chain rule:
MATH

Then, we put in the proper functions and we have the answer:
MATH

2. Find MATH and MATH when $dw$ is as follows:
 MATH

Answer:

To find MATH we hold $s$ constant and use the following chain rule:
MATH

MATH

MATH

To find MATH we hold $t$ constant and use the following chain rule:
MATH

MATH

MATH

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