3.4 Chain Rule. Prerequisite Knowledge Product Rule Quotient Rule Power Rule Special Derivatives:

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Presentation transcript:

3.4 Chain Rule

Prerequisite Knowledge Product Rule Quotient Rule Power Rule Special Derivatives:

Special Derivatives

Chain Rule with Numbers

Chain Rule With Calculus Why is this helpful? Suppose you had to differentiate:

Example:

Examples

Chain Rule Some special derivatives that come from the Chain Rule:

Homework Pg. 162 # [6]

Applications (Day 2) Example: Air is being pumped into a spherical balloon so that the radius is increasing at a rate of 2 inches per second. At what rate is the volume increasing after 3 seconds? After 10 seconds?

Example 2 A 15 foot tall pole that was initially vertical begins to fall in such a way that the angle relative to the ground is decreasing at a rate of 3 degrees per second. At what rate is the top of the pole getting closer to the ground after 4 seconds?

Homework (2) Pg. 164 #

Homework (3) Pg. 164 # 163, 165