**CHAIN RULE**:

**F(x) = f(g(x))**

F'(x) = f'(g(x))g'(x)

F'(x) = f'(g(x))g'(x)

**1. Differentiate.**

2. f(x) xe

2. f(x) xe

^{-3x}**a) find f'**

**b) find f"**

c) determine the interval(s) where f is increasing

c) determine the interval(s) where f is increasing

(-infinity, 1/3)

**d) determine the interval(s) where f is concave up**

(2/3, infinity)

**3. Given the equation below, solve for y and differentiate**

**x**

^{2}+ y^{2}= 25

IMPLICIT means that it's SUGGESTED without having it IN YOUR FACE!

IMPLICIT means that it's SUGGESTED without having it IN YOUR FACE!

**A circle isn't a function but we can still find the derivative for it by looking at one section of it.**

**The next scribe is MARK**

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