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Answer :
Final answer:
The derivative of the function y = 12x^5 + 3x^4 + 7x^3 + x^2 - 9x + 6 is y' = 60x^4 + 12x^3 + 21x^2 + 2x - 9. This is found by applying the basic power rule of calculus.
Explanation:
The question is asking you to determine the derivative of the given polynomial function y = 12x^5 + 3x^4 + 7x^3 + x^2 - 9x + 6. Finding the derivative involves applying the power rule, which is a basic theorem in calculus which states that the derivative of x^n, where n is any real number, is n*x^(n-1).
By applying the power rule to this particular function, the derivative y' is calculated as follows: 12*5x^(5-1) + 3*4x^(4-1) + 7*3x^(3-1) + 2x^(2-1) - 9. Hence, the derivative, y', of the original function is given by y' = 60x^4 + 12x^3 + 21x^2 + 2x - 9. Comparing this with the options, it corresponds to option 'a'.
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