High School

Find the derivative of [tex]y = 12x^4 + \frac{5}{x^7} - 8\csc{x}[/tex].

A. [tex]y' = 48x^3 + \frac{35}{x^8} + 8\csc{x}\cot{x}[/tex]
B. [tex]y' = 48x^3 - \frac{35}{x^8} - 8\csc{x}\cot{x}[/tex]
C. [tex]y' = 48x^3 - \frac{5}{7x^6} + 8\csc{x}\cot{x}[/tex]
D. [tex]y' = 48x^3 - \frac{35}{x^6} + 8\csc{x}\cot{x}[/tex]

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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