d dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Many like to remember that the derivative of a product is the derivative of the first function times dx (x)(x)] f'(x) g(x) + f(x). g'(x) derivative of first second first derivative of second For the given equation y = 2x(5x2 - 1), if we let f(x) = 2x and g(x) = 5x21, then y = 2x(5x2. g(x) = 5x21 as the second function. Note that since y is the product of two differentiable functions, we can use the product rule to find As a precursor to using the product rule, complete the following statements. If f(x) = 2x, then f'(x) = 2 If g(x)=5x21, then g'(x) = 10x 2 10x Step 2 With f(x) = 2x, f'(x) = 2, g(x) = 5x - 1, and g'(x) = 10x, we are now ready to substitute these continue to simplify.