Question

Find the first derivative of the function f(x) = (8x³ + x⁻⁴)⁷cot(2-5x).

Answer 1

To find the first derivative of the function f(x) = (8x³ + x⁻⁴)⁷cot(2-5x), apply the chain rule and product rule. First, find the derivative of the function inside the parentheses, then apply the derivative of the cotangent function, and finally, multiply the two derivatives together.

Step-by-step explanation:

To find the first derivative of the function f(x) = (8x³ + x⁻⁴)⁷cot(2-5x), you need to apply the chain rule and product rule.

1. First, find the derivative of the function inside the parentheses: d/dx(8x³ + x⁻⁴) = 24x² - 4x⁻⁵.
2. Next, apply the derivative of the cotangent function: d/dx(cot(2-5x)) = -csc²(2-5x) * (-5).
3. Finally, multiply the two derivatives together: f'(x) = (24x² - 4x⁻⁵) * (-csc²(2-5x) * (-5)).