In the given equation y = 2x(5x2-1) we have the product of two differentiable functions of x: 2x and (5x Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies. dx [f(x)(x)] = f'(x)9(x) + f(x)9'(x) Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function. f'(x) g(x) + f(x). derivative of first second dx (x)(x)]-de g'(x) first derivative of second For the given equation y = 2x(5x2-1), If we let f(x) 2x and g(x) = 5x2-1, then y = 2x(5x2-1) f(x) g(x). In other words, we can define f(x) = 2x as the first function and g(x) = 5x-1 as the second function. dy Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or dx As a precursor to using the product rule, complete the following statements. If f(x) 2x, then f(x) I If g(x) 5x2-1, then g'(x) =