BC Calculus: §3.6 Chain Rule



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:


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: