Derivatives from graphs Use the figure to find the following derivatives. <IMAGE>
d/dx (xg(x)) | x=2

Verified step by step guidance

1. Step 1: Recognize that you need to find the derivative of the product of two functions, x and g(x), at x = 2. This requires using the product rule for differentiation.
2. Step 2: Recall the product rule formula: if you have two functions u(x) and v(x), then the derivative of their product is given by (u(x)v(x))' = u'(x)v(x) + u(x)v'(x).
3. Step 3: Identify u(x) = x and v(x) = g(x). Compute the derivatives: u'(x) = 1 and v'(x) = g'(x).
4. Step 4: Apply the product rule: (xg(x))' = 1 * g(x) + x * g'(x).
5. Step 5: Evaluate the expression at x = 2: substitute x = 2 into the expression 1 * g(x) + x * g'(x) to find the derivative at that point. Use the graph to find the values of g(2) and g'(2).