find the derivative of y3x272Solution To solve for this deri

Solution

To solve for this derivative, we use the product rule: y\' = f\'(x)g(x) + f(x)g\'(x) --> where f(x) and g(x) are two different functions. First we take the derivative of f(x), which is f\'(x) and multiply that by g(x). Then, we multiply f(x) with the derivative of g(x), which is g\'(x). y = (3x^2 - 7)^2 = (3x^2 - 7)(3x^2 - 7) --> here, we treat f(x) as 3x^2 - 7 and g(x) as 3x^2 - 7. Solving for the derivative: y\' = (6x)(3x^2 - 7) + (6x)(3x^2 - 7) y\' = 18x^3 - 42x + 18x^3 - 42x --> Now, we group like terms y\' = 18x^3 + 18x^3 - 42x - 42x y\' = 36x^3 -84x Hope this helps! :-)