Question

Find the derivative of f(x) = 8tanx - 6cotx.

Answer 1

To find the derivative of f(x) = 8tanx - 6cotx, apply the differentiation rules for tangent and cotangent to get f'(x) = 8sec^2x + 6csc^2x.

Step-by-step explanation:

The subject of the question is to find the derivative of the function f(x) = 8tanx - 6cotx. To find the derivative of this function, we need to use the rules of differentiation, particularly the derivatives of the tangent and cotangent functions. The derivative of tanx is sec2x, and the derivative of cotx is -csc2x. So, the derivative of f(x) can be found using these derivatives.

Steps to find the derivative:

1. Identify the function to differentiate: f(x) = 8tanx - 6cotx.
2. Apply the derivative to tanx: The derivative is 8sec2x.
3. Apply the derivative to cotx: The derivative is -6(-csc2x), simplifying to +6csc2x.
4. Combine the derivatives: The final derivative of f(x) is f'(x) = 8sec2x + 6csc2x.