# BC Calculus: §3.6 Chain Rule

• Class: 5H: BC Calculus
• Author: Peter Atlas
• Text: Calculus Finney, Demana, Waits, Kennedy

Given the following tabular information about differentiable functions $$f(x)$$ and $$g(x) \text{ at }x = 2$$ and $$x = 3$$:

x$$f(x)$$$$g(x)$$$$f'(x)$$$$g'(x)$$
282$$\frac{1}{3}$$-3
33-4e5
Determine the value of $$\frac{d}{dx}$$ of:
• $$2f(x) \text{ at }x = 2$$
• $$f(x) + g(x) \text{ at }x = 3$$
• $$f(x) \cdot g(x) \text{ at }x =$$3
• $$\frac{f(x)}{g(x)} \text{ at }x = 2$$
• $$f(g(x)) \text{ at }x = 2$$

Given $$f(x)$$ and $$g(x)$$ are differentiable functions over the real numbers, $$f'(x) = - f(x)$$ and $$g'(x) = g(x) + 1$$, and:

x$$f(x)$$$$g(x)$$
-321
-212
-130
0-13
1-2-1
20-2
Evaluate $$\frac{d}{dx}$$ of the following:
• $$f(g(x)) \text{ at }x = -1$$
• $$g(f(x)) \text{ at }x = -2$$
• $$f(x)\cdot g(x - 1) \text{ at }x = 1$$
• $$\frac{g(x)}{f(x+5)} \text{ at }x = -3$$