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Answer :
The derivative of the function y = 12x⁴ + 5/x⁷ - 8csc(x) is y' = 48x³ - 35/x⁸ - 8csc(x)cot(x). Option b is the answer.
The subject of this question is the differentiation of an algebraic and trigonometric function in mathematics. We are given a function y = 12x⁴ + 5/x⁷ - 8csc(x) and are asked to find the derivative of this function. The correct derivative is found by applying the power rule to 12x⁴ and 5/x⁷, and the product rule combined with the chain rule to -8csc(x). Using these rules, the correct derivative of the given function is y' = 48x³ - 35/x⁸ - 8csc(x)cot(x).
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