Answer :
Final answer:
The derivative of the function y = (7x^4 - 4x^2 + 4)^4 using the chain rule is 4*(7x^4 - 4x^2 + 4)^3 * (28x^3 - 8x), which none of the provided options correctly represent.
Explanation:
The question asks us to find the derivative of the function y = (7x^4 - 4x^2 + 4)^4. To solve this, we will use the chain rule of calculus, which is a technique for differentiating compositions of functions. We first recognize our outer function as u^4 where u = 7x^4 - 4x^2 + 4, and then we differentiate the inner function u with respect to x. The derivative of u is 28x^3 - 8x.
Applying the chain rule, we multiply the derivative of the outer function with respect to u, which is 4u^3, by the derivative of u with respect to x, giving us 4*(7x^4 - 4x^2 + 4)^3 * (28x^3 - 8x). None of the provided options correctly represents the derivative of the function because they are not in the form that applies the chain rule properly to this function.
