Answer :
Final answer:
To find the derivative of the function y = 7 + 9x^4, we differentiate each term separately. The derivative of a constant term like 7 is 0, and the derivative of 9x^4 is 36x^3. The derivative of the function y = 7 + 9x^4 is found by applying the power rule, leading to an answer of 36x^3, which matches option C).
Explanation:
Differentiation is a method used to compute the rate of change of a function f(x) with respect to its input x . This rate of change is known as the derivative of f with respect to x . To find the derivative of this function, we apply the basic rules of differentiation. The derivative of a constant is 0, so the derivative of 7 is 0. For the term 9x^4, we apply the power rule which states that the derivative of x^n is n*x^(n-1). Hence, the derivative of 9x^4 is 9*4x^(4-1) which simplifies to 36x^3.
Therefore, the correct option that represents the derivative of the function y = 7 + 9x^4 is C) 36x^3.
